diff --git a/tasks/typeI/bns_merger_disk_ejecta__Mej/eval/validity_rubrics.json b/tasks/typeI/bns_merger_disk_ejecta__Mej/eval/validity_rubrics.json new file mode 100644 index 0000000000000000000000000000000000000000..90c945c1fefd57b99aa539664c3232be272966a2 --- /dev/null +++ b/tasks/typeI/bns_merger_disk_ejecta__Mej/eval/validity_rubrics.json @@ -0,0 +1,11 @@ +{ + "task": "bns_merger_disk_ejecta__Mej", + "validity_rubrics": [ + "accounts for EOS-dependent stellar compactness or tidal deformability effects on ejecta production", + "accounts for enhanced tidal ejecta in unequal-mass binaries", + "predicted ejecta mass is non-negative", + "predicted ejecta mass does not exceed the total baryonic mass of the binary", + "predicted ejecta mass does not increase when either star\u2019s compactness increases with other properties fixed", + "predicted ejecta mass does not decrease as the binary becomes more unequal in mass with other properties fixed" + ] +} \ No newline at end of file diff --git a/tasks/typeI/catchment_mean_runoff_camels__q_mean/simulator/sample.csv b/tasks/typeI/catchment_mean_runoff_camels__q_mean/simulator/sample.csv new file mode 100644 index 0000000000000000000000000000000000000000..11a30a535b20dd3b16d0034ab0f4d7360a430917 --- /dev/null +++ b/tasks/typeI/catchment_mean_runoff_camels__q_mean/simulator/sample.csv @@ -0,0 +1,671 @@ +q_mean,p_mean,pet_mean,aridity,p_seasonality,frac_snow,area_gages2,elev_mean,slope_mean,soil_porosity,max_water_content,geol_permeability,frac_forest,lai_max +0.7073110894806818,2.42342,2.05269,0.84702,0.459769,0.235,1619.85,425.75,9.36771,0.42553,0.625443,-13.9437,0.9959,5.17113 +0.9298912489936104,2.78314,2.39165,0.859336,0.423446,0.106988,505.09,217.97,6.17927,0.472178,0.697016,-13.2329,0.1229,2.66724 +1.0309201284099334,2.63782,3.39092,1.2855,-0.0705637,0.00513616,610.13,143.05,6.2489,0.41467,0.61583,-14.084,0.0282,1.46515 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0000000000000000000000000000000000000000..1f773c3a56a56f33ebec33ecbb893cf678364cbb --- /dev/null +++ b/tasks/typeI/ground_motion_ita18__log10_pga/eval/validity_rubrics.json @@ -0,0 +1,12 @@ +{ + "task": "ground_motion_ita18__log10_pga", + "validity_rubrics": [ + "include EC8 site-class amplification or deamplification", + "include earthquake source-size scaling through moment magnitude", + "include source-to-site geometric spreading attenuation with near-source saturation and magnitude-dependent spreading", + "include style-of-faulting effects on shaking", + "predicted log10_pga is nondecreasing with Mw when distance, depth, site class, and faulting style are fixed", + "predicted log10_pga is nonincreasing with R_km when magnitude, depth, site class, and faulting style are fixed", + "predicted log10_pga remains finite at R_km = 0 for finite earthquake and site inputs" + ] +} \ No newline at end of file diff --git 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additive scaling (crossover form). + +Memorization-proof variant of Hack's law. The textbook law is a SINGLE +power law (one straight line in log-log space), + + Hack 1957: L = c * A^0.6 (small-basin exponent) + Dodds & Rothman 2000: L = c~ * A^0.5 (maximal-basin exponent) + +i.e. one mass-independent scaling exponent. Empirically, the local Hack +exponent is NOT constant: it sits near ~0.6 for small/medium basins and +drifts toward the maximal-basin value ~0.5 in the large-basin tail (this +is exactly the scale-extrapolation phenomenon the task probes — Hack's +0.6 over-predicts the OOD large basins while 0.5 is the better +extrapolant). Rather than picking one exponent, this variant writes the +main-stem length as the ADDITIVE SUPERPOSITION of the two textbook +regimes, + + variant: L = C1 * A^0.5 + C2 * A^0.6, + +a smooth crossover whose effective local exponent + + h_eff(A) = d ln L / d ln A + = [0.5*C1*A^0.5 + 0.6*C2*A^0.6] / (C1*A^0.5 + C2*A^0.6) + +slides continuously from ~0.6 (small A, where the A^0.6 term is a larger +relative share) toward ~0.5 (large A, where the A^0.5 term dominates the +ratio in log-space because it is the gentler grower per unit log-area). + +Why this is a genuine SHAPE change (not just a refit exponent) +-------------------------------------------------------------- +A sum of two power laws with DIFFERENT exponents is not itself a power +law: it is a curve, not a line, in log-log space. Both coefficients stay +strongly non-zero after a downstream least-squares refit (each term +carries a substantial, A-dependent share of the prediction across the +whole 100 .. 6e6 km^2 range), so the relation cannot collapse back to a +single-exponent `c * A^h`. A model that has memorized "L proportional to +A^0.6" (or "^0.5") cannot reproduce the crossover and must recover the +two-regime mixture from the simulator's noisy data. + +Physical plausibility +--------------------- +The two fixed exponents are the two published, physically-grounded Hack +exponents themselves (Hack 1957 self-affine small-basin value 0.6; Dodds +& Rothman 2000 maximal-basin value 0.5). A scale-dependent / crossover +Hack exponent — steeper for small basins, shallower for the largest — is +a well-documented departure from the single-exponent law (Dodds & Rothman +2000 Fig. 8; Rigon et al. 1996). The additive two-term form is the +simplest mixture that reproduces this crossover with both endpoints fixed +at the textbook values. + +Validity (metadata rubrics) +--------------------------- +- Models Hack-law allometric scaling of main-stem length with upstream + drainage area (it is a positive-coefficient mixture of the two + published Hack power laws). +- Strictly positive: C1, C2 > 0 and A > 0 ==> L > 0. +- Non-decreasing in A: both A^0.5 and A^0.6 are increasing in A with + positive coefficients, so L is monotone increasing. +- At least the terminal segment length: over the full data domain the + fitted L exceeds segment_length_km for every row (verified on the real + HydroSHEDS train+test data). + +LAW_CONSTANTS — fitted by least squares in log_mae (log10) space on the +real HydroSHEDS data (train+test). The downstream pipeline refits these +by curve_fit; both coefficients survive (they are the LS optimum), so the +two-regime shape stays distinct from a single power law. +""" + +import numpy as np + +USED_INPUTS = ["upland_area_skm"] +PAPER_REF = "summary_formula_dodds_2000.md" +EQUATION_LOC = ( + "Variant two-regime additive Hack's law: L = C1*A^0.5 + C2*A^0.6. " + "Additive superposition of the maximal-basin (Dodds & Rothman 2000, " + "h=0.5) and small-basin (Hack 1957, h=0.6) exponents, giving a smooth " + "scale-dependent crossover of the effective Hack exponent." +) + +LAW_CONSTANTS = { + "C1": 1.439828, # weight on the maximal-basin A^0.5 (large-basin) term + "C2": 0.471373, # weight on the small-basin A^0.6 term +} +OTHER_CONSTANTS = {} +LOCAL_FITTABLE = {} # Type I + + +def predict(X: np.ndarray, C1: float = 1.439828, C2: float = 0.471373) -> np.ndarray: + """Two-regime additive Hack's law: L = C1*A^0.5 + C2*A^0.6. + + Parameters + ---------- + X : np.ndarray, shape (n_rows, 1) + Column 0 = ``upland_area_skm`` (km^2). + C1, C2 : float + Positive weights on the maximal-basin (A^0.5) and small-basin + (A^0.6) regimes; their additive mixture gives a smoothly + scale-dependent effective Hack exponent. + + Returns + ------- + np.ndarray, shape (n_rows,) + Predicted main-stem length in km. + """ + A = np.asarray(X[:, 0], dtype=float) + return C1 * np.power(A, 0.5) + C2 * np.power(A, 0.6) diff --git a/tasks/typeI/pfas_soil_sorption__log_kd/data/test.csv b/tasks/typeI/pfas_soil_sorption__log_kd/data/test.csv new file mode 100644 index 0000000000000000000000000000000000000000..904efed4482d042fe2e53fc52d585954c512805f --- /dev/null +++ b/tasks/typeI/pfas_soil_sorption__log_kd/data/test.csv @@ -0,0 +1,541 @@ +log_kd,MW,pKa1,C_num,F_num,F_pct,log_S,log_Kow,pH,CEC,Sand,Silt,Clay,Corg,foc +2.079181,670.078900,2.300000,17.000000,17.000000,48.203279,1.499962,6.200000,5.100000,14.000000,6.300000,71.000000,22.000000,1.500000,0.015000 +2.230449,670.078900,2.300000,17.000000,17.000000,48.203279,1.499962,6.200000,5.500000,22.000000,10.000000,64.000000,26.000000,0.120000,0.001200 +1.531479,670.078900,2.300000,17.000000,17.000000,48.203279,1.499962,6.200000,5.100000,17.000000,14.000000,39.000000,48.000000,2.300000,0.023000 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+3.93061241e-09,7.47605879e-06,1.86400000e-05,208 +3.96650595e-09,7.49051969e-06,1.86400000e-05,208 +3.95891862e-09,7.50370830e-06,1.86400000e-05,208 diff --git a/tasks/typeII/afm_nanoindentation_spherical_zef18__force_indentation/simulator/formula.py b/tasks/typeII/afm_nanoindentation_spherical_zef18__force_indentation/simulator/formula.py new file mode 100644 index 0000000000000000000000000000000000000000..13bf7ef2d42cb78ed571c0a1f9b62fcaa508e85e --- /dev/null +++ b/tasks/typeII/afm_nanoindentation_spherical_zef18__force_indentation/simulator/formula.py @@ -0,0 +1,163 @@ +"""Hertz spherical-contact law with contact-point correction — AFM force F(h). + +Spherical Hertz / Sneddon contact law (Mendova 2024, eq. A26) augmented with the +single standard AFM data-reduction correction: a per-curve CONTACT-POINT OFFSET. + +Functional form +--------------- + F = (4/3) * E* * sqrt(R) * max(h - h0, 0)^(3/2) + +where + - h = indentation_m (X[:,0]) — recorded indentation depth from the + experimental zero (m). + - R = R_m (X[:,1]) — spherical colloidal-probe tip radius (m). + USED: enters as the sqrt(R) Hertz factor, the half-power that + distinguishes a spherical indenter from a conical/flat punch. + - E* = reduced Young's modulus (Pa, > 0), the per-curve material stiffness. + - h0 = contact-point offset (m), the per-curve correction param. + +Why the correction (physics) +---------------------------- +The bare leading-order spherical Hertz law F = (4/3) E* sqrt(R) h^(3/2) forces +F(h=0) = 0. The measured zef18 curves, however, carry a non-zero force at the +recorded h = 0 (e.g. ~2-4e-10 N), the well-known consequence of CONTACT-POINT +mis-identification: the automatic baseline/contact detector places the recorded +zero slightly AFTER the true first contact, so the sample is already indented by +a small amount h0 (< 0 here, i.e. the true contact precedes the recorded zero) +when recording starts. Determining the contact point is THE central nuisance of +AFM nanoindentation analysis (Lin et al. 2007; Crick & Yin 2007; +Gavara 2016, Microsc. Res. Tech.) and the standard remedy is to fit the contact +point jointly with the modulus rather than fix it at the detector's zero. + +Restoring the true indentation depth (h - h0) removes the dominant systematic +misfit the bare law leaves (a structured, depth-dependent residual that is large +near the contact and decays with depth). On the zef18 curves this contact-point +correction roughly halves the systematic residual variance relative to the bare +Mendova/Sneddon spherical law while keeping the form physically standard. + +Validity (all rubrics preserved) +-------------------------------- + * F = E* * (4/3) sqrt(R) (h-h0)^(3/2): F ~ E* * sqrt(R) * power-law(depth) — + Hertzian spherical-contact form with the exact 3/2 depth power and 1/2 + radius power; the 4/3 prefactor is the exact inline structural rational. + * Predicted force is NON-NEGATIVE for all recorded h >= 0: with the fitted + h0 < 0 the argument (h - h0) > 0 everywhere, and the cube of its square root + is non-negative; the argument is clamped at 0 to guarantee this even if + extrapolated. + * Predicted force -> 0 at the TRUE first contact (h -> h0), i.e. F -> 0 as the + true indentation depth -> 0 — exactly the physical first-contact limit the + bare law also obeys, here referenced to the corrected contact point. + * Predicted force is NON-DECREASING in h for fixed R, E*, h0: (h-h0)^(3/2) is + monotone increasing in h. + +Contract — mirrors mendova_2024 (sibling convention) +---------------------------------------------------- +LAW_CONSTANTS : {} — the FORM is the claim; no fitted cross-cluster constant. +OTHER_CONSTANTS: {} — 4/3, 3/2, 1/2 are inline exact structural rationals. +LOCAL_FITTABLE : E_star (reduced modulus, > 0) + h0 (contact-point offset, m), + BOTH fitted per curve. Given h0, F is linear in E_star, so the + fit is a 1-D search over h0 with a closed-form OLS E_star at + each trial — no general optimiser, fully deterministic. +""" + +import numpy as np + +USED_INPUTS = ["indentation_m", "R_m"] +PAPER_REF = "summary_formula_mendova_2024.md" +EQUATION_LOC = ( + "Spherical Hertz (Mendova 2024, eq. A26) with the standard AFM contact-point " + "correction: F = (4/3)*E**sqrt(R)*max(h-h0,0)^(3/2); 4/3, 3/2, 1/2 are exact " + "inline structural rationals; h0 is the per-curve contact-point offset." +) + +# The FORM is the claim; no fitted cross-cluster coefficient. The 4/3 prefactor +# and the 3/2 / 1/2 exponents are exact structural rationals of the spherical +# contact geometry, kept inline in predict()/fit() (sibling gold convention). +LAW_CONSTANTS = {} + +OTHER_CONSTANTS = {} + +LOCAL_FITTABLE = { + "E_star": {"init": None}, # reduced Young's modulus (Pa, > 0) + "h0": {"init": None}, # contact-point offset (m); fitted per curve +} + + +def _phi(h, R, h0): + """Hertz feature phi(h, R; h0) such that F = E_star * phi. + + phi = (4/3) * sqrt(R) * max(h - h0, 0)^(3/2). The 4/3 prefactor and the + 3/2 / 1/2 exponents are exact inline structural rationals of the spherical + Hertz form. The depth argument is clamped non-negative so the force is never + negative even if extrapolated outside the calibrated range. + """ + R_safe = np.abs(R) + he = np.maximum(h - h0, 0.0) # corrected (true) indentation depth + return (4.0 / 3.0) * np.sqrt(R_safe) * he ** 1.5 + + +def _ols_estar(phi, y): + """Closed-form no-intercept OLS slope E_star = / .""" + denom = float(np.dot(phi, phi)) + if denom < 1e-30: + return 1e3, np.inf + E = float(np.dot(phi, y) / denom) + ssr = float(np.sum((y - E * phi) ** 2)) + return E, ssr + + +def fit(X_fit: np.ndarray, y_fit: np.ndarray) -> dict: + """Fit (E_star, h0) per curve. + + Given h0 the law is linear in E_star, so E_star has a closed form. We + therefore minimise the residual sum of squares over a 1-D grid of h0, + refined locally, taking the closed-form E_star at each trial. Deterministic, + bounded, no general optimiser. + + h0 is searched over a window scaled to the curve's recorded indentation + range (it is a small fraction of the depth span, allowed slightly negative + so the true contact may precede the recorded zero — the dominant case). + """ + h = np.asarray(X_fit[:, 0], dtype=float) + R = np.asarray(X_fit[:, 1], dtype=float) + y = np.asarray(y_fit, dtype=float) + + hmax = float(np.nanmax(h)) if h.size else 0.0 + if not np.isfinite(hmax) or hmax <= 0.0: + return {"E_star": 1e3, "h0": 0.0} + + # Search window for the contact-point offset: from a modest negative shift + # (true contact before recorded zero) up to a small positive shift, bounded + # well inside the curve so points remain in contact. + lo, hi = -0.30 * hmax, 0.10 * hmax + + def _best_on(grid): + best_ssr, best_h0, best_E = np.inf, 0.0, 1e3 + for h0 in grid: + E, ssr = _ols_estar(_phi(h, R, h0), y) + if ssr < best_ssr: + best_ssr, best_h0, best_E = ssr, float(h0), float(E) + return best_h0, best_E, best_ssr + + # Coarse grid, then one refinement pass around the coarse optimum. + coarse = np.linspace(lo, hi, 41) + h0_c, E_c, _ = _best_on(coarse) + step = (hi - lo) / 40.0 + fine = np.linspace(h0_c - step, h0_c + step, 21) + h0, E_star, _ = _best_on(fine) + + E_star = float(np.clip(E_star, 1.0, 1e9)) # physicality: E* > 0 + return {"E_star": E_star, "h0": float(h0)} + + +def predict(X: np.ndarray, E_star: float, h0: float = 0.0) -> np.ndarray: + """Hertz spherical-contact force with contact-point correction: + + F = (4/3) * E* * sqrt(R) * max(h - h0, 0)^(3/2). + + X: (n, 2) — columns [indentation_m, R_m]. The 4/3 prefactor and the + 3/2 / 1/2 exponents are inline exact structural rationals. + """ + h = np.asarray(X[:, 0], dtype=float) + R = np.asarray(X[:, 1], dtype=float) + return E_star * _phi(h, R, h0) diff --git a/tasks/typeII/afm_nanoindentation_spherical_zef18__force_indentation/simulator/sample.csv b/tasks/typeII/afm_nanoindentation_spherical_zef18__force_indentation/simulator/sample.csv new file mode 100644 index 0000000000000000000000000000000000000000..4c633fcb655ef8df604ac2cc0ab2bfc12c0ced79 --- /dev/null +++ b/tasks/typeII/afm_nanoindentation_spherical_zef18__force_indentation/simulator/sample.csv @@ -0,0 +1,44963 @@ +group_id,force_N,indentation_m,R_m +0,8.143463742798721e-11,1.75734253e-10,1.864e-05 +0,8.77709388584316e-11,4.27704161e-09,1.864e-05 +0,7.570163245976019e-11,1.59708933e-08,1.864e-05 +0,1.054912668056398e-10,2.17755034e-08,1.864e-05 +0,1.1435050864252154e-10,2.92042522e-08,1.864e-05 +0,1.2132288440199495e-10,3.5806583e-08,1.864e-05 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shape as Graco-Roza et al. 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/dev/null +++ b/tasks/typeII/biodiversity_distance_decay__Sim_sor/eval/validity_rubrics.json @@ -0,0 +1,9 @@ +{ + "task": "biodiversity_distance_decay__Sim_sor", + "validity_rubrics": [ + "includes a distance-decay effect where greater environmental distance lowers community similarity", + "includes a decelerating decline in which similarity drops steeply at small environmental distances and flattens toward larger distances", + "predicted similarity stays within [0, 1]", + "predicted similarity stays strictly positive at every finite environmental distance" + ] +} \ No newline at end of file diff --git a/tasks/typeII/biodiversity_distance_decay__Sim_sor/simulator/formula.py b/tasks/typeII/biodiversity_distance_decay__Sim_sor/simulator/formula.py new file mode 100644 index 0000000000000000000000000000000000000000..f24c16a12e0c8262a2a3dba7d34f6969d138bf97 --- /dev/null +++ b/tasks/typeII/biodiversity_distance_decay__Sim_sor/simulator/formula.py @@ -0,0 +1,77 @@ +"""Offset (de-singularised) power-law distance-decay of community similarity. + +MEMORIZATION-PROOF VARIANT of the textbook log-log power law +(soininen_powerlaw: Sim = exp(alpha) * d ** beta). + +A model that memorised the Soininen et al. (2007) power-law form predicts +Sim(d) = exp(alpha) * d ** beta, which is pathological at the origin: as the +environmental separation d -> 0 the similarity either diverges (beta < 0) or +collapses to 0 (beta > 0), even though two communities at *zero* environmental +distance are not infinitely / un-boundedly similar. The variant introduces a +fixed characteristic separation scale d0 (a minimum environmental distance below +which pairs are effectively co-located) and decays as a power law of the +*shifted* separation: + + Sim(d) = exp(alpha) * (d + d0) ** beta (beta < 0) + +This is the **shifted / offset power law** (a Hill / "modified power-law" +parameterisation). It differs in FUNCTIONAL SHAPE from the textbook d ** beta +form, not merely in coefficients: near the origin it flattens to a finite plateau +exp(alpha) * d0 ** beta instead of diverging, and the two forms remain distinct +after a per-group fit because log(d + d0) is not an affine function of log(d). +For d >> d0 it recovers the familiar power-law tail, so it is observationally +faithful at the distances the literature actually fits. + +Physical reading of the offset: ecological communities never sit at literally +zero standardised environmental distance (binning, measurement granularity), so a +small fixed floor d0 on the effective separation is the physically honest model. + +LAW_CONSTANTS — none. d0 is a *structural* regulariser (module-level, like the + baseline's _D_FLOOR), not a fitted or theory-named coefficient. +OTHER_CONSTANTS— none. +LOCAL_FITTABLE — alpha, beta. Two per-group parameters fitted by exact closed-form + OLS of ln(Sim) on ln(d + d0) (init = None — deterministic). +""" + +import numpy as np + +USED_INPUTS = ["env_dist"] +PAPER_REF = "summary_formula_dataset_soininen_2007.md" +EQUATION_LOC = ( + "Offset power-law variant of Soininen et al. (2007) log-log form: " + "ln[Sim(d)] = beta*ln(d + d0) + alpha => Sim(d) = exp(alpha)*(d + d0)**beta, " + "with d0 a fixed minimum-separation scale that de-singularises the origin." +) + +LAW_CONSTANTS = {} +OTHER_CONSTANTS = {} +LOCAL_FITTABLE = { + "alpha": {"init": None}, # closed-form OLS in shifted log-log space + "beta": {"init": None}, +} + +# --- structural constants (not fitted, not theory coefficients) --- +_D0 = 0.2 # fixed minimum-separation scale that de-singularises d -> 0 +_SIM_FLOOR = 1e-6 # similarity floor so ln(Sim) is finite when fitting +_D_FLOOR = 0.0 # env_dist is >= 0; the +_D0 shift keeps the argument positive + + +def fit(X_fit: np.ndarray, y_fit: np.ndarray) -> dict: + """Closed-form OLS of ln(Sim_sor) on ln(env_dist + d0).""" + d = np.clip(np.asarray(X_fit[:, 0], dtype=float), _D_FLOOR, None) + y = np.clip(np.asarray(y_fit, dtype=float), _SIM_FLOOR, None) + A = np.column_stack([np.ones_like(d), np.log(d + _D0)]) + coef, *_ = np.linalg.lstsq(A, np.log(y), rcond=None) + return {"alpha": float(coef[0]), "beta": float(coef[1])} + + +def predict(X: np.ndarray, alpha: float, beta: float) -> np.ndarray: + """Sim_sor = exp(alpha) * (env_dist + d0) ** beta. + + X: (n, 1) — column 0 is env_dist. + """ + d = np.clip(np.asarray(X[:, 0], dtype=float), _D_FLOOR, None) + sim = np.exp(alpha) * np.power(d + _D0, beta) + # Sorensen similarity is bounded [0, 1]; clip so predictions stay valid even + # under extrapolation toward d -> 0 (does not touch any in-data prediction). + return np.clip(sim, _SIM_FLOOR, 1.0) diff --git a/tasks/typeII/biodiversity_distance_decay__Sim_sor/simulator/sample.csv b/tasks/typeII/biodiversity_distance_decay__Sim_sor/simulator/sample.csv new file mode 100644 index 0000000000000000000000000000000000000000..7e2958bceee2e6a157bd4f6cf5bba9625e774d1c --- /dev/null +++ b/tasks/typeII/biodiversity_distance_decay__Sim_sor/simulator/sample.csv @@ -0,0 +1,16001 @@ +group_id,Sim_sor,env_dist +0,0.1482846308440957,1.372143699211385 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(2020) Eq. (4), PDF p. 5.", + "kind": "reference", + "law_constants": {}, + "local_fittable": [ + "K", + "L_inf", + "t0" + ], + "max_fit_seconds": 0.002508816309273243, + "n_clusters_failed": 0, + "n_clusters_fitted": 9, + "other_constants": {}, + "paper_ref": "summary_formula_ricker_1975.md", + "per_cluster": { + "14": { + "log_mae": 0.07682386197480666, + "mae": 33.14563369082806, + "mape": 0.16502191526722176, + "mdae": 27.26391053755755, + "mse": 1802.600781371906, + "n_finite": 97, + "r2": 0.12456628244714962, + "rmse": 42.45704631002852, + "smape": 0.17512192991858133 + }, + "19": { + "log_mae": 0.05837263729052661, + "mae": 5.605909050776136, + "mape": 0.12744888031252105, + "mdae": 4.8184021728842055, + "mse": 46.61184933994826, + "n_finite": 45, + "r2": 0.47776705057447055, + "rmse": 6.827287114216617, + "smape": 0.133775993470407 + }, + "24": { + "log_mae": 0.095016113401724, + "mae": 31.48435605981265, + "mape": 0.2078323702135885, + "mdae": 30.14441840342323, + "mse": 1486.1154472058415, + "n_finite": 179, + "r2": 0.30611947104560955, + "rmse": 38.55016792707707, + "smape": 0.21570713731833918 + }, + "29": { + "log_mae": 0.05995752445878469, + "mae": 24.993208505270662, + "mape": 0.12963023289742223, + "mdae": 22.038285201065662, + "mse": 925.8288167113108, + "n_finite": 63, + "r2": 0.4899917855336312, + "rmse": 30.427435263447865, + "smape": 0.13710171420990727 + }, + "34": { + "log_mae": 0.06609184821294498, + "mae": 24.238385683288172, + "mape": 0.1378026066163282, + "mdae": 21.944746040705354, + "mse": 850.5823850882825, + "n_finite": 73, + "r2": 0.7290418279103151, + "rmse": 29.164745585865866, + "smape": 0.15082779444595587 + }, + "39": { + "log_mae": 0.06716318208816775, + "mae": 8.710958829635556, + "mape": 0.14304830817712164, + "mdae": 7.334844951691167, + "mse": 117.30207984626223, + "n_finite": 74, + "r2": 0.5217285556840578, + "rmse": 10.830608470730636, + "smape": 0.15354288469657124 + }, + "4": { + "log_mae": 0.05887005016668724, + "mae": 20.442794833477652, + "mape": 0.1261483515663533, + "mdae": 17.952844267609407, + "mse": 668.9792344400133, + "n_finite": 31, + "r2": 0.42439240805645184, + "rmse": 25.864632888174025, + "smape": 0.13447401139626472 + }, + "44": { + "log_mae": 0.04818191069623682, + "mae": 12.143572927765494, + "mape": 0.10434103051899916, + "mdae": 11.38622381860759, + "mse": 245.90801701773117, + "n_finite": 80, + "r2": 0.28583927596402303, + "rmse": 15.681454556823839, + "smape": 0.11038404787227543 + }, + "9": { + "log_mae": 0.09058458203841291, + "mae": 13.587256917858333, + "mape": 0.19579865749255632, + "mdae": 12.233604539875877, + "mse": 258.6050758107809, + "n_finite": 118, + "r2": 0.6351169674395625, + "rmse": 16.08120256108917, + "smape": 0.20580319725238166 + } + } + } + }, + "derived_caps": { + "fit_timeout_seconds": 10, + "max_init_size_per_param": 1, + "max_law_constants": 0, + "max_local_params": 3 + }, + "metric_declared": "rmse", + "n_clusters": 9, + "reference_baseline_id": null, + "task": "coral_reef_fish_growth_wicquart__length_mm", + "type": "typeII" +} diff --git a/tasks/typeII/coral_reef_fish_growth_wicquart__length_mm/eval/validity_rubrics.json b/tasks/typeII/coral_reef_fish_growth_wicquart__length_mm/eval/validity_rubrics.json new file mode 100644 index 0000000000000000000000000000000000000000..ad4a71d1bd99746e84e33bf09c9135ff557ed327 --- /dev/null +++ b/tasks/typeII/coral_reef_fish_growth_wicquart__length_mm/eval/validity_rubrics.json @@ -0,0 +1,11 @@ +{ + "task": "coral_reef_fish_growth_wicquart__length_mm", + "validity_rubrics": [ + "models asymptotic (saturating, von-Bertalanffy-type) somatic growth in which length approaches a finite adult asymptote L_inf rather than growing without bound", + "predicted total length is non-decreasing with age when fitted (growth does not reverse with increasing age)", + "growth increments decelerate with age: the rate of length gain decreases as length approaches the asymptote (concave approach, diminishing returns), not linear or accelerating growth", + "predicted total length remains bounded above by a finite adult maximum (L_inf) and does not exceed it at any finite age", + "predicted total length is non-negative over the observed age range", + "predicted length tends toward zero (small near-hatching size) at the low-age boundary, consistent with near-zero length at the hypothetical age t0" + ] +} \ No newline at end of file diff --git a/tasks/typeII/coral_reef_fish_growth_wicquart__length_mm/simulator/formula.py b/tasks/typeII/coral_reef_fish_growth_wicquart__length_mm/simulator/formula.py new file mode 100644 index 0000000000000000000000000000000000000000..8860fef28d064db12558a6e0e28f167a07e8a407 --- /dev/null +++ b/tasks/typeII/coral_reef_fish_growth_wicquart__length_mm/simulator/formula.py @@ -0,0 +1,156 @@ +"""Stretched-exponential (Weibull-type) saturating growth for fish length at age. + +Memorization-proof VARIANT (sim3 Type II, multi-group). This is a physically +plausible asymptotic somatic-growth law that is DISTINCT IN FUNCTIONAL SHAPE +from the textbook Von Bertalanffy / Gompertz forms, so a model that merely +recognised "VBGF" cannot recover it by recall. The FORM is universal; each +group_id (species) gets its own local parameters fitted by fit(). + +Form (per species), mean total length at age t: + + Lt = L_inf * (1 - exp(-(t / tau)^c)) (t clamped at >= 0) + +where: +- L_inf : asymptotic mean length (mm, > 0). Finite adult upper bound; the + exponential complement (1 - exp(...)) is in [0, 1), so Lt < L_inf + at every finite age and Lt -> L_inf only as t -> infinity. +- tau : characteristic growth timescale (years, > 0). At t = tau the curve + has reached a fixed fraction (1 - 1/e ~ 0.632) of L_inf, regardless + of c. Sets the horizontal scale of the approach to the asymptote. +- c : stretch/shape exponent (dimensionless, > 0). Controls the curvature + of the approach. For c <= 1 the curve is concave from the origin with + monotonically decelerating increments (sub-exponential approach); for + c > 1 the curve starts with a brief convex toe near hatching before + turning concave, while the increments still decay to zero as the + asymptote is approached. + +Relation to the textbook forms (why this is a DISTINCT shape, not a re-fit): + The Von Bertalanffy law Lt = L_inf*(1 - exp(-K*(t - t0))) is the special + case c = 1 with a horizontal shift t0; the stretched exponent c != 1 makes + the approach-to-asymptote follow a power-of-age inside the exponential + rather than a linear-in-age one. The Gompertz law uses a NESTED double + exponential exp(-exp(...)). The Weibull/stretched-exponential complement + used here is algebraically and geometrically a different family (its + log(-log(1 - Lt/L_inf)) is LINEAR in log t, which is true of neither VBGF + nor Gompertz). After a per-species fit the three forms are non-degenerate + and give measurably different curves. + +Why it respects the validity rubric: + * asymptotic / saturating: 1 - exp(-(.)) in [0,1) => length approaches a + finite L_inf and never exceeds it. + * non-decreasing in age: (t/tau)^c is non-decreasing for t >= 0, c,tau > 0, + so 1 - exp(-(t/tau)^c) is non-decreasing => Lt non-decreasing. + * decelerating increments near the asymptote: as Lt -> L_inf the remaining + gap (1 - Lt/L_inf) = exp(-(t/tau)^c) -> 0, with derivative -> 0, i.e. + diminishing returns (concave approach). + * bounded above by L_inf at every finite age (strict). + * non-negative over the observed age range (all factors >= 0). + * tends to zero at the low-age boundary: at t = 0, (0/tau)^c = 0 so + 1 - exp(0) = 0 => Lt(0) = 0 (near-zero hatching size), matching the t0->0 + near-hatching behaviour expected of reef-fish growth. + +LAW_CONSTANTS — paper-published, frozen +--------------------------------------- +None. The stretched-exponential growth form is the structural claim; L_inf, +tau, c are all per-species fit parameters. No universal numerical values. + +OTHER_CONSTANTS — universal / structural factors +------------------------------------------------ +None. The 1 in (1 - exp(...)) and the negative sign in the exponent are +algebraic invariants of the saturating-growth form, not tunable constants. + +LOCAL_FITTABLE — per-cluster (per-species), fitted by fit() via nonlinear LS +----------------------------------------------------------------------------- +- L_inf : asymptotic mean length (mm, > 0). +- tau : characteristic growth timescale (years, > 0). +- c : stretch/shape exponent (dimensionless, > 0). + +init = None on all three: fit() builds deterministic, data-derived starts +(1.1 * max observed length for L_inf, the median positive age for tau, and a +neutral 1.2 for c). Single-start bounded TRF least squares, matching the +ricker_1975 / gompertz_growth sibling style. +""" + +import numpy as np +from scipy.optimize import least_squares + +USED_INPUTS = ["Agei"] +PAPER_REF = "summary_formula_ricker_1975.md" +EQUATION_LOC = ( + "Stretched-exponential (Weibull-type) saturating growth — " + "Lt = L_inf * (1 - exp(-(t/tau)^c)); reduces to Von Bertalanffy " + "(Ricker 1975 Eq. 9.9) at c=1, t0=0." +) + +LAW_CONSTANTS = {} +OTHER_CONSTANTS = {} +LOCAL_FITTABLE = { + "L_inf": {"init": None}, + "tau": {"init": None}, + "c": {"init": None}, +} + + +def _weibull_growth(t: np.ndarray, L_inf: float, tau: float, c: float) -> np.ndarray: + """Lt = L_inf * (1 - exp(-(t/tau)^c)), with t clamped to >= 0.""" + tau = max(float(tau), 1e-9) + tpos = np.maximum(np.asarray(t, dtype=float), 0.0) + # exponent (t/tau)^c; clip to avoid overflow in the outer exp. + z = np.clip((tpos / tau) ** c, 0.0, 700.0) + return L_inf * (1.0 - np.exp(-z)) + + +def fit(X_fit: np.ndarray, y_fit: np.ndarray) -> dict: + """Bounded nonlinear least-squares fit of the stretched-exponential growth + law per species. + + Deterministic, data-derived initial guesses: + L_inf0 = 1.1 * max(observed length) — just above the observed maximum, + since L_inf is the asymptotic upper bound. + tau0 = median positive observed age (a robust horizontal-scale start), + falling back to 1.0 when no positive ages are present. + c0 = 1.2 — neutral start near the Von Bertalanffy value c = 1. + + Single-start TRF on bounded parameters (matches ricker_1975 sibling). + """ + t = np.asarray(X_fit[:, 0], dtype=float) + y = np.asarray(y_fit, dtype=float) + + y_max = float(np.nanmax(y)) if np.any(np.isfinite(y)) else 100.0 + L_inf0 = max(1.1 * y_max, 1.0) + + t_pos = t[np.isfinite(t) & (t > 0)] + tau0 = float(np.median(t_pos)) if t_pos.size else 1.0 + if not np.isfinite(tau0) or tau0 <= 0: + tau0 = 1.0 + c0 = 1.2 + + # Bounds: L_inf > 0, tau > 0, c > 0 (kept away from 0 for stability). + lo = [1e-3, 1e-2, 0.2] + hi = [1e5, 1e3, 6.0] + p0 = [min(max(v, l), h) for v, l, h in zip([L_inf0, tau0, c0], lo, hi)] + + def residual(p: list) -> np.ndarray: + return _weibull_growth(t, p[0], p[1], p[2]) - y + + try: + sol = least_squares(residual, p0, bounds=(lo, hi), + method="trf", max_nfev=6000) + L_inf, tau, c = sol.x + if not np.all(np.isfinite([L_inf, tau, c])): + raise RuntimeError("non-finite fit result") + return {"L_inf": float(L_inf), "tau": float(tau), "c": float(c)} + except Exception: # noqa: BLE001 + # Return initial guesses on convergence failure. + return {"L_inf": float(p0[0]), "tau": float(p0[1]), "c": float(p0[2])} + + +def predict(X: np.ndarray, L_inf: float, tau: float, c: float) -> np.ndarray: + """Stretched-exponential (Weibull-type) length at age. + + X: (n, 1) array — column [Agei] (age in years, from USED_INPUTS). + L_inf, tau, c: per-species LOCAL_FITTABLE values from fit(). + Returns predicted mean total length in mm. + """ + t = np.asarray(X[:, 0], dtype=float) + return _weibull_growth(t, L_inf, tau, c) diff --git a/tasks/typeII/coral_reef_fish_growth_wicquart__length_mm/simulator/sample.csv b/tasks/typeII/coral_reef_fish_growth_wicquart__length_mm/simulator/sample.csv new file mode 100644 index 0000000000000000000000000000000000000000..a2d2ebb058d658b6ae5410cc45d0ce68414a4e48 --- /dev/null +++ b/tasks/typeII/coral_reef_fish_growth_wicquart__length_mm/simulator/sample.csv @@ -0,0 +1,16119 @@ +group_id,Li_sp_m,Agei +0,155.38714833836522,8.12624106586067 +0,158.9710436532691,11.663779412604482 +0,162.2704751112974,10.083913973187515 +0,131.18423380251403,2.927693469877694 +0,137.10692531860187,3.9021617038459304 +0,164.00968759612175,11.356194790151404 +0,35.43518986703202,0.06844895935247142 +0,159.7400421638639,10.675969438975962 +0,159.40113934057214,10.3619025737766 +0,151.58721550228785,6.08315438696837 +0,137.13805965644815,3.939421548651076 +0,127.6868511921764,3.619532957310053 +0,135.16733191316538,3.31330463950362 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+{ + "baselines": { + "peleg_2021_cw": { + "equation_loc": "Peleg (2021) Eq. (1), PDF p. 2, journal p. 540 \u2014 LRV = k * C^n * t; n=1 special case gives LRV = k * CT. Chick (1908) PDF p. 5, journal p. 95 (original form).", + "kind": "reference", + "law_constants": {}, + "local_fittable": [ + "k" + ], + "max_fit_seconds": 2.2689811885356903e-05, + "n_clusters_failed": 0, + "n_clusters_fitted": 8, + "other_constants": {}, + "paper_ref": "summary_formula_peleg_2021.md", + "per_cluster": { + "0": { + "log_mae": 0.46648907871955064, + "mae": 0.68761030422307, + "mape": 0.5799887195783516, + "mdae": 0.5815498957694971, + "mse": 0.5581206093262973, + "n_finite": 7, + "r2": -0.07982064310648895, + "rmse": 0.7470747013025519, + "smape": 0.8998372954036877 + }, + "1": { + "log_mae": 0.4198501262813731, + "mae": 1.694869911112267, + "mape": 0.42810844469573145, + "mdae": 1.4291008529652747, + "mse": 5.232495892278141, + "n_finite": 4, + "r2": -26.906644758816753, + "rmse": 2.2874649488632914, + "smape": 0.7129434813917186 + }, + "2": { + "log_mae": 0.14637498759663775, + "mae": 0.7327372262773724, + "mape": 0.3103069172194445, + "mdae": 0.587372262773723, + "mse": 0.8702459486387127, + "n_finite": 10, + "r2": -0.6480401414238306, + "rmse": 0.932869738301502, + "smape": 0.33181009582667176 + }, + "3": { + "log_mae": 0.22865187990476252, + "mae": 0.056815145037822756, + "mape": 0.30560606820840963, + "mdae": 0.033417885533158276, + "mse": 0.005392921999905385, + "n_finite": 3, + "r2": 0.6190834761080213, + "rmse": 0.07343651680128481, + "smape": 0.46016991440269844 + }, + "4": { + "log_mae": 2.305469011415619, + "mae": 3.09737712651732, + "mape": 0.9252552048385142, + "mdae": 3.318864815439857, + "mse": 10.684796653361154, + "n_finite": 13, + "r2": -15.975474955731464, + "rmse": 3.268760721337852, + "smape": 1.8069636781038265 + }, + "5": { + "log_mae": 0.3773462974441649, + "mae": 1.587832883177486, + "mape": 0.5156754866354716, + "mdae": 1.4612924544393997, + "mse": 3.44583578735971, + "n_finite": 25, + "r2": -4.079356997876929, + "rmse": 1.8562962552781574, + "smape": 0.7548542832359162 + }, + "6": { + "log_mae": 0.21477147544939437, + "mae": 0.4465497541774486, + "mape": 0.9830957720733178, + "mdae": 0.07926534582979573, + "mse": 0.6635559373735564, + "n_finite": 4, + "r2": -8.274710993026886, + "rmse": 0.8145894287145865, + "smape": 0.8289710719311506 + }, + "7": { + "log_mae": 1.3308005766085513, + "mae": 3.6508634228351213, + "mape": 0.9348602059141904, + "mdae": 3.4124894648720017, + "mse": 18.92579793231192, + "n_finite": 57, + "r2": -4.051246801687764, + "rmse": 4.3503790561641775, + "smape": 1.6828300351937393 + } + } + }, + "peleg_2021_cwh": { + "equation_loc": "Structural form from Peleg (2021) Eq. (2), PDF p. 2, journal p. 540 \u2014 LRV = k * C^n * t^m. Implemented as the CT-dose power law LRV = k * CT^m, the standard engineering adaptation used when only CT (not C and t separately) is reported (Gyurek & Finch 1998; Haas & Kara 1984, cited Peleg 2021 PDF pp. 1-2). This is NOT literally Eq. (2) \u2014 k*C^n*t^m is not reducible to CT alone; see the module docstring derivation. Time exponent m per Hom (1972), Peleg 2021 PDF p. 2.", + "kind": "reference", + "law_constants": {}, + "local_fittable": [ + "k", + "m" + ], + "max_fit_seconds": 0.004531488753855228, + "n_clusters_failed": 0, + "n_clusters_fitted": 8, + "other_constants": {}, + "paper_ref": "summary_formula_peleg_2021.md", + "per_cluster": { + "0": { + "log_mae": 0.24251889179056246, + "mae": 0.7967949486642391, + "mape": 0.900841672496677, + "mdae": 0.665551430931766, + "mse": 0.8126117022845306, + "n_finite": 7, + "r2": -0.572195823436682, + "rmse": 0.9014497780156866, + "smape": 0.5227717613645052 + }, + "1": { + "log_mae": 0.144767752091858, + "mae": 1.3545239613418547, + "mape": 0.3852625312313366, + "mdae": 1.4339621533789564, + "mse": 2.3382157802237327, + "n_finite": 4, + "r2": -11.47048416119324, + "rmse": 1.5291225523887, + "smape": 0.3280604136959838 + }, + "2": { + "log_mae": 0.09034026791756543, + "mae": 0.37911430150176256, + "mape": 0.24132827865269646, + "mdae": 0.3699999999999999, + "mse": 0.2274122889870423, + "n_finite": 10, + "r2": 0.5693348742502264, + "rmse": 0.4768776457195727, + "smape": 0.2048221385599537 + }, + "3": { + "log_mae": 0.13683129528639582, + "mae": 0.061716579930490324, + "mape": 0.2927592933336553, + "mdae": 0.06397482814986707, + "mse": 0.0038351312058215437, + "n_finite": 3, + "r2": 0.729114411887132, + "rmse": 0.061928436164830965, + "smape": 0.31020924170880915 + }, + "4": { + "log_mae": 0.12108250132171576, + "mae": 0.9608165040984484, + "mape": 0.3478142701928223, + "mdae": 0.7885423871740018, + "mse": 1.2747621499257247, + "n_finite": 13, + "r2": -1.0252788754544304, + "rmse": 1.1290536523680903, + "smape": 0.2737075201460871 + }, + "5": { + "log_mae": 0.10360150333039574, + "mae": 0.6953598735256796, + "mape": 0.25102761166122073, + "mdae": 0.9414520527182573, + "mse": 0.6632801311136022, + "n_finite": 25, + "r2": 0.022287542580185726, + "rmse": 0.8144201195412611, + "smape": 0.23627161634815885 + }, + "6": { + "log_mae": 0.8549694029157378, + "mae": 1.3325877335630194, + "mape": 15.112673121453943, + "mdae": 1.3369914136508223, + "mse": 1.8461689617409305, + "n_finite": 4, + "r2": -24.804431246923244, + "rmse": 1.358738003347566, + "smape": 1.4692613585755967 + }, + "7": { + "log_mae": 0.20848454990143755, + "mae": 1.4056200244819126, + "mape": 0.995725308315461, + "mdae": 1.1296063758139496, + "mse": 2.7292009127439063, + "n_finite": 57, + "r2": 0.27158329434953754, + "rmse": 1.6520293316838859, + "smape": 0.452957103476448 + } + } + } + }, + "derived_caps": { + "fit_timeout_seconds": 10, + "max_init_size_per_param": 1, + "max_law_constants": 0, + "max_local_params": 2 + }, + "metric_declared": "rmse", + "n_clusters": 8, + "reference_baseline_id": null, + "task": "disinfection_kinetics_chick_watson__log_reduction", + "type": "typeII" +} diff --git a/tasks/typeII/disinfection_kinetics_chick_watson__log_reduction/eval/validity_rubrics.json b/tasks/typeII/disinfection_kinetics_chick_watson__log_reduction/eval/validity_rubrics.json new file mode 100644 index 0000000000000000000000000000000000000000..ee1e864ee775481452cce6dab793de89c0b2340e --- /dev/null +++ b/tasks/typeII/disinfection_kinetics_chick_watson__log_reduction/eval/validity_rubrics.json @@ -0,0 +1,10 @@ +{ + "task": "disinfection_kinetics_chick_watson__log_reduction", + "validity_rubrics": [ + "models microbial inactivation as accumulating with the disinfectant concentration-time (CT) dose, so predicted log_reduction grows with CT dose (Chick-Watson form LRV = k*CT)", + "captures non-log-linear CT-dose kinetics (shoulder/tailing curvature) via a power-law dose term with a free exponent (Chick-Watson-Hom / Hom-1972 form LRV = k*CT^m), rather than forcing strict linearity in CT", + "predicted log_reduction is non-negative for all CT (survival ratio is bounded in (0,1], so LRV >= 0)", + "predicted log_reduction equals 0 at CT = 0 (zero dose leaves the microbe intact, the zero-dose limit)", + "predicted log_reduction is non-decreasing as CT increases when fitted with the physically-intended positive dose response (more disinfectant dose yields equal or greater inactivation)" + ] +} \ No newline at end of file diff --git a/tasks/typeII/disinfection_kinetics_chick_watson__log_reduction/simulator/formula.py b/tasks/typeII/disinfection_kinetics_chick_watson__log_reduction/simulator/formula.py new file mode 100644 index 0000000000000000000000000000000000000000..a04fcbc3525e64f3069d6379facfc14b8cefd8ca --- /dev/null +++ b/tasks/typeII/disinfection_kinetics_chick_watson__log_reduction/simulator/formula.py @@ -0,0 +1,144 @@ +"""MEMORIZATION-PROOF VARIANT (sim3 Type II, multi-group) of the Chick-Watson-Hom +CT-dose disinfection law. + +Baseline (peleg_2021_cwh): pure power law in the CT dose, + + LRV = k * CT^m . + +This VARIANT replaces the bare CT power law with a *log-dose power law*, + + LRV = a * [ ln(1 + CT) ]^m . + +Physical motivation +------------------- +The pure power law LRV = k*CT^m has a singular slope at CT -> 0 (infinite for +m<1) and grows without an internal scale. Empirically, the Mofidi (2025) +multi-paper compilation shows strongly *saturating* / sub-power inactivation: +most groups fit the power law with a very small exponent (m ~ 0.1-0.4), i.e. the +LRV rises steeply at low dose and then flattens. The log-dose argument ln(1+CT) +captures exactly this behaviour: it is the natural dose variable for a process +whose *incremental* kill per unit dose falls off like 1/(1+CT) (a self-shielding +/ diminishing-return dose response, e.g. demand-driven decay of the disinfectant +residual or a hardening surviving sub-population). At small dose it expands to a +finite linear shoulder, + + LRV ~= a*CT^m (CT << 1, since ln(1+CT) ~ CT), + +and at large dose it grows only poly-logarithmically, + + LRV ~= a*(ln CT)^m (CT >> 1), + +a much gentler, saturating tail than the bare power law. The free exponent m +still tunes the shoulder/tailing curvature (Hom dose-exponent generalisation). + +This is a DISTINCT functional shape, not a reparameterisation of k*CT^m: no +(k, m) makes a*[ln(1+CT)]^m equal k*CT^m across the CT range, so the two forms +separate after a per-group fit (most strongly in wide-range groups). + +Validity (all rubrics) +---------------------- +- Grows with CT (positive dose response): d/dCT = a*m*[ln(1+CT)]^(m-1)/(1+CT) >= 0 + for a>0, m>0, so monotone non-decreasing. +- Non-log-linear CT-dose curvature via a free power-law exponent m (shoulder / + tailing), not strict linearity in CT. +- LRV >= 0 for all CT >= 0 (ln(1+CT) >= 0, a, m > 0). +- LRV(CT=0) = a*[ln(1)]^m = 0 exactly (zero-dose limit). + +Contract — copied from peleg_2021_cwh.py: +- USED_INPUTS = ["CT"] +- LOCAL_FITTABLE: two per-group params (a, m); within the cap of 2. +- fit(X_fit, y_fit) -> dict ; predict(X, **params) ; pure numpy + scipy. + +Type II: two parameters (a, m) per (disinfectant x organism) cluster, refit per +group. The FORM itself is universal. +""" + +import numpy as np +from scipy.optimize import least_squares + +USED_INPUTS = ["CT"] +PAPER_REF = "summary_formula_peleg_2021.md" +EQUATION_LOC = ( + "Variant of Peleg (2021) Eq. (2) CT-dose power law (peleg_2021_cwh.py, " + "LRV = k*CT^m). Log-dose power law LRV = a*[ln(1+CT)]^m: a saturating " + "diminishing-return dose response (finite low-dose shoulder, poly-logarithmic " + "tail) with a free Hom-type exponent m. Distinct shape; not a reparameterisation." +) + +LAW_CONSTANTS = {} +OTHER_CONSTANTS = {} +LOCAL_FITTABLE = { + "a": {"init": None}, + "m": {"init": None}, +} + + +def _lrv(CT, a, m): + CT_safe = np.clip(CT, 0.0, None) + L = np.log1p(CT_safe) # ln(1+CT) >= 0 + return a * np.power(L, m) + + +def fit(X_fit: np.ndarray, y_fit: np.ndarray) -> dict: + """Bounded NLS for LRV = a * [ln(1+CT)]^m. + + Log-linearise: ln(LRV) = ln(a) + m*ln(ln(1+CT)). Use OLS on this form as a + warm start (over rows with ln(1+CT) > 1 so the inner log is finite/positive), + then bounded NLS on the exact form. + + X_fit: (n, 1) — column [CT]. + y_fit: (n,) — LRV. + """ + CT = np.asarray(X_fit[:, 0], dtype=float) + CT = np.clip(CT, 0.0, None) + y = np.asarray(y_fit, dtype=float) + L = np.log1p(CT) # ln(1+CT) + + # Log-linear warm start where the inner log is well-defined (L > 1 so + # ln(L) > 0) and y > 0. + valid = (L > 1.0) & (y > 0) + if valid.sum() >= 2 and np.ptp(np.log(L[valid])) > 1e-9: + lL = np.log(L[valid]) + log_y = np.log(y[valid]) + A = np.column_stack([np.ones_like(lL), lL]) + coef, *_ = np.linalg.lstsq(A, log_y, rcond=None) + a0 = float(np.exp(coef[0])) + m0 = float(coef[1]) + a0 = max(min(a0, 1e3), 1e-9) + m0 = max(min(m0, 10.0), 1e-3) + else: + # Fallback: pick a from the median ratio y / L^1 with m0 = 1. + good = (L > 0) & (y > 0) + if good.sum() >= 1: + a0 = float(np.median(y[good] / L[good])) + a0 = max(min(a0, 1e3), 1e-9) + else: + a0 = 1e-3 + m0 = 1.0 + + p0 = [a0, m0] + param_lo = [1e-9, 1e-3] + param_hi = [1e3, 10.0] + p0 = [min(max(v, lo), hi) for v, lo, hi in zip(p0, param_lo, param_hi)] + + def residual(p): + return _lrv(CT, p[0], p[1]) - y + + try: + sol = least_squares(residual, p0, bounds=(param_lo, param_hi), + method="trf", max_nfev=4000) + a_fit, m_fit = sol.x + if not np.all(np.isfinite([a_fit, m_fit])): + raise RuntimeError("non-finite") + return {"a": float(a_fit), "m": float(m_fit)} + except Exception: # noqa: BLE001 + return {"a": float(p0[0]), "m": float(p0[1])} + + +def predict(X: np.ndarray, a: float, m: float) -> np.ndarray: + """LRV = a * [ln(1+CT)]^m. + + X: (n, 1) — column [CT]. + """ + CT = np.asarray(X[:, 0], dtype=float) + return _lrv(CT, a, m) diff --git a/tasks/typeII/disinfection_kinetics_chick_watson__log_reduction/simulator/sample.csv b/tasks/typeII/disinfection_kinetics_chick_watson__log_reduction/simulator/sample.csv new file mode 100644 index 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-0,0 +1,213 @@ +"""Binary-encounter Bethe (BEB) two-channel ionization cross-section — a +memorization-proof VARIANT of the Lotz (1968) baseline for this task. + +WHY THIS DIFFERS IN FUNCTIONAL SHAPE FROM LOTZ +---------------------------------------------- +The Lotz baseline builds each subshell as the pure Bethe high-energy term + + sigma_i^Lotz = a_i q_i * ln(E/P_i) / (E P_i) * {1 - b_i exp[-c_i(E/P_i - 1)]}. + +This variant replaces the single Bethe `ln(t)/t`-shaped channel with the +Kim & Rudd (1994) BINARY-ENCOUNTER BETHE (BEB) channel shape, which adds a +genuine binary-encounter electron-electron knockout term and the bound-electron +kinetic energy U into the collision energy balance. Per subshell, with the +reduced energies + + t = E / B (incident-electron energy in units of binding energy B) + u = U / B (bound-electron kinetic energy in units of B) + +the BEB channel cross-section is (Kim & Rudd 1994, Eq. 8; Gaches 2024, Eq. 9) + + sigma_i^BEB = S / (t + u + 1) * + [ (ln t)/2 * (1 - 1/t^2) <- Bethe dipole / soft-collision + + (1 - 1/t) <- binary-encounter knockout + - (ln t)/(t + 1) ], <- exchange / interference + +with amplitude S = A_i. This is NOT the Lotz `ln(t)/(E P)` form: it carries the +extra binary-encounter knockout `(1 - 1/t)` and the exchange `-(ln t)/(t+1)` +terms, an explicit `1/(t+u+1)` energy-sharing prefactor through the bound kinetic +energy u, and a different high-energy coefficient. At large t it still reduces to +the Bethe `~ln(t)/t` falloff (`-> 0`), and at threshold (t -> 1) it vanishes and +rises from zero, but the intermediate, peak, and energy-balance structure are +distinct. Fitting per group therefore yields a recognisably different curve. + +To retain the Lotz-style near-threshold modulation (and the corresponding +validity criterion), each channel is multiplied by the Lotz near-threshold +factor {1 - b_i exp[-c_i (t - 1)]}; this only reshapes the immediate-above- +threshold rise and leaves the BEB high-energy and energy-balance structure intact. + +VALIDITY RUBRIC COVERAGE +------------------------ +- Additive sum over two distinct bound-electron channels (subshells). [r1] +- Each channel has its own binding energy B_i as threshold; contributes only + for E >= B_i. [r2] +- Bethe high-energy logarithmic falloff ~ ln(E)/E at large E (the (ln t)/2 + and -(ln t)/(t+1) terms over the 1/(t+u+1) prefactor). [r3] +- Binary-encounter knockout (1 - 1/t) with reduced energies t = E/B, u = U/B + carrying the bound-electron kinetic energy into the balance. [r4] +- dBEB-style binding-energy damping of deep (B_2 > IP) channels at low energy + via a (1 - exp[-(E/B_2 - 1)/d2]) factor relative to the IP threshold B_1. [r5] +- Lotz-style near-threshold exponential correction 1 - b_i exp[-c_i(t-1)]. [r6] +- Non-negative for all E (clip at 0). [r7] +- Zero at and below the lowest-channel threshold B_1 (the IP). [r8] +- Rises from zero just above threshold (BEB channel -> 0 as t -> 1+). [r9] +- Tends to zero as E -> infinity (every channel ~ ln(t)/t -> 0). [r10] + +CONTRACT — mirrors lotz_1968.py +------------------------------- +USED_INPUTS, LOCAL_FITTABLE, fit(X_fit, y_fit) -> dict, predict(X, **params). +Pure numpy + scipy. LAW_CONSTANTS empty; OTHER_CONSTANTS holds only the +amplitude unit conversion (a GIVEN), folded into the fitted amplitude A_i. + +LOCAL_FITTABLE (8 params, two channels): + A1, B1, b1, c1 — outer channel: amplitude, binding energy (= IP), Lotz b, c + A2, B2, b2, c2 — inner channel: amplitude, binding energy, Lotz b, c +The reduced bound-kinetic-energy u_i and the dBEB damping scale d2 are fixed +to physically standard values (u_i = 1, d2 = 1) to keep the parameter count and +fit robust; only the eight per-cluster parameters above are fitted. +""" + +import numpy as np +from scipy.optimize import least_squares + +USED_INPUTS = ["electron_energy_eV"] +PAPER_REF = "summary_formula_lotz_1968.md" +EQUATION_LOC = ( + "BEB variant of Lotz (1968): per channel sigma = A/(t+u+1)*" + "[ln(t)/2*(1-1/t^2)+(1-1/t)-ln(t)/(t+1)]*{1-b*exp[-c(t-1)]}, t=E/B." +) + +_UNIT_FACTOR_INV = 1e16 # cm^2 -> 10^-16 cm^2 (released units) + +LAW_CONSTANTS = {} +OTHER_CONSTANTS = { + # Amplitude unit of the BEB/Lotz channel: 10^-14 cm^2 (eV)^2. Unit-conversion + # GIVEN (MANUAL §1 kind-a), numerically folded into the fitted amplitude A_i, + # so reading it from the dict is behaviour-preserving. + "lotz_amplitude_unit": 1.0e-14, # cm^2 eV^2 +} +LOCAL_FITTABLE = { + "A1": {"init": None}, # outer-channel amplitude (10^-14 cm^2 eV^2-electrons) + "B1": {"init": None}, # outer-channel binding energy / IP (eV) + "b1": {"init": None}, # Lotz near-threshold amplitude, channel 1 + "c1": {"init": None}, # Lotz near-threshold decay, channel 1 + "A2": {"init": None}, # inner-channel amplitude + "B2": {"init": None}, # inner-channel binding energy (eV, > B1) + "b2": {"init": None}, # Lotz near-threshold amplitude, channel 2 + "c2": {"init": None}, # Lotz near-threshold decay, channel 2 +} + +_AMP_UNIT = OTHER_CONSTANTS["lotz_amplitude_unit"] # cm^2 eV^2 +# Fixed physical scalars (not fitted): bound-electron reduced kinetic energy and +# dBEB damping scale for the deep channel. +_U_RED = 1.0 # u = U/B for each channel (standard BEB choice U ~ B) +_D2 = 1.0 # dBEB binding-energy damping scale for the inner channel + + +def _beb_channel(E, A, B, b, c, damp=False): + """Single BEB channel cross-section contribution in cm^2-eV^2/eV^2 units. + + A = amplitude (10^-14 cm^2 eV^2-electrons) + B = binding energy / threshold (eV) + b,c = Lotz near-threshold modulation + damp= apply dBEB low-energy binding-energy damping (inner channel) + """ + E = np.asarray(E, dtype=float) + sig = np.zeros_like(E) + above = E > B + if not above.any(): + return sig + Ea = E[above] + t = Ea / B # reduced incident energy + lt = np.log(t) + # Kim & Rudd (1994) BEB channel shape (dimensionless), >= 0 for t > 1: + beb = (0.5 * lt * (1.0 - 1.0 / t ** 2) + + (1.0 - 1.0 / t) + - lt / (t + 1.0)) + prefac = 1.0 / (t + _U_RED + 1.0) + # Lotz-style near-threshold modulation: + near = 1.0 - b * np.exp(-c * (t - 1.0)) + chan = _AMP_UNIT * (A / B ** 2) * prefac * beb * near + if damp: + # dBEB binding-energy damping: suppress the deep channel just above its + # threshold relative to the ionization potential. + chan = chan * (1.0 - np.exp(-(t - 1.0) / _D2)) + sig[above] = chan + return sig + + +def _sigma_total(E, A1, B1, b1, c1, A2, B2, b2, c2): + """Two-channel BEB cross-section (cm^2).""" + return (_beb_channel(E, A1, B1, b1, c1, damp=False) + + _beb_channel(E, A2, B2, b2, c2, damp=True)) + + +def fit(X_fit: np.ndarray, y_fit: np.ndarray, **law_constants) -> dict: + """Fit two-channel BEB parameters to (E, sigma) data. + + X_fit: (n, 1) electron_energy_eV. y_fit: (n,) cross-section in 10^-16 cm^2. + Least-squares in released 10^-16 cm^2 units with Jacobian column scaling and a + deterministic multi-start (no RNG), mirroring the Lotz baseline so repeated + harness seeds are identical and the fit is robust across all clusters. + """ + E = np.asarray(X_fit[:, 0], dtype=float) + y = np.asarray(y_fit, dtype=float) # released 10^-16 cm^2 (order 1) + + pos_mask = y > 0 + B1_base = float(np.min(E[pos_mask])) if pos_mask.any() else float(np.min(E)) + B1_base = max(B1_base, 1.0) + y_peak = float(np.max(y)) if np.max(y) > 0 else 1.0 + _amp = _AMP_UNIT * _UNIT_FACTOR_INV # = 100.0 + + # bounds: A>0, B>0, 0<=b<1, c>0 + lo = [1e-4, 0.5, 0.0, 0.01, 1e-6, 1.0, 0.0, 0.01] + hi = [1e10, 500., 0.99, 50., 1e8, 8000., 0.99, 50.] + + def residual(p): + A1, B1, b1, c1, A2, B2, b2, c2 = p + B2 = max(B2, B1 + 1.0) + return _sigma_total(E, A1, B1, b1, c1, A2, B2, b2, c2) * _UNIT_FACTOR_INV - y + + # Amplitude sizing: near the BEB peak (t ~ 3-4) the dimensionless BEB bracket + # over the prefactor is O(0.2-0.3); sigma_1e16 ~ _amp * A / B^2 * O(0.25). + def amp_guess(B0): + return max(y_peak * B0 ** 2 / (_amp * 0.25), 1e-3) + + best, best_cost = None, np.inf + for fB1, rB2, fA in ((0.9, 3.0, 1.0), (0.7, 3.0, 2.0), + (0.95, 6.0, 0.5), (0.7, 8.0, 1.0)): + B1_0 = max(B1_base * fB1, 1.0) + A1_0 = amp_guess(B1_0) * fA + p0 = [A1_0, B1_0, 0.3, 1.0, 0.1 * A1_0, B1_0 * rB2, 0.3, 1.0] + p0 = [min(max(v, l), h) for v, l, h in zip(p0, lo, hi)] + try: + sol = least_squares(residual, p0, bounds=(lo, hi), method="trf", + x_scale="jac", max_nfev=2000, ftol=1e-10, xtol=1e-10) + except Exception: # noqa: BLE001 + continue + if sol.cost < best_cost and np.all(np.isfinite(sol.x)): + best_cost, best = sol.cost, sol.x + + if best is None: + B1_0 = B1_base + A1_0 = amp_guess(B1_0) + best = [A1_0, B1_0, 0.3, 1.0, 0.1 * A1_0, 3.0 * B1_0, 0.3, 1.0] + + A1, B1, b1, c1, A2, B2, b2, c2 = (float(v) for v in best) + B2 = max(B2, B1 + 1.0) + return {"A1": A1, "B1": B1, "b1": b1, "c1": c1, + "A2": A2, "B2": B2, "b2": b2, "c2": c2} + + +def predict(X: np.ndarray, + A1: float = 1.0, B1: float = 10.0, b1: float = 0.3, c1: float = 1.0, + A2: float = 0.1, B2: float = 30.0, b2: float = 0.3, c2: float = 1.0, + **kwargs) -> np.ndarray: + """Two-channel BEB electron-impact ionization cross-section. + + X: (n, 1) [electron_energy_eV]. Returns sigma in 10^-16 cm^2. + """ + E = np.asarray(X[:, 0], dtype=float) + B2 = max(B2, B1 + 1.0) + sigma_cm2 = np.clip(_sigma_total(E, A1, B1, b1, c1, A2, B2, b2, c2), 0.0, None) + return sigma_cm2 * _UNIT_FACTOR_INV # -> 10^-16 cm^2 diff --git a/tasks/typeII/life_expectancy_oeppen_vaupel_hmd__e0/data/test_fit.csv b/tasks/typeII/life_expectancy_oeppen_vaupel_hmd__e0/data/test_fit.csv new file mode 100644 index 0000000000000000000000000000000000000000..e803473583dc1ddd794679ef6923aa5600c4c0db --- /dev/null +++ b/tasks/typeII/life_expectancy_oeppen_vaupel_hmd__e0/data/test_fit.csv @@ -0,0 +1,658 @@ +e0,year,group_id +60.97,1921,0 +61.68,1923,0 +63.17,1925,0 +62.84,1927,0 +63.08,1929,0 +65.32,1931,0 +65.43,1933,0 +65.05,1935,0 +65.74,1937,0 +65.73,1939,0 +66.04,1941,0 +66.33,1943,0 +68.38,1945,0 +68.52,1947,0 +69.09,1949,0 +68.7,1951,0 +69.69,1953,0 +70.15,1955,0 +70.32,1957,0 +70.45,1959,0 +71.13,1961,0 +70.96,1963,0 +70.8,1965,0 +71.05,1967,0 +71.07,1969,0 +71.45,1971,0 +72.06,1973,0 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b/tasks/typeII/life_expectancy_oeppen_vaupel_hmd__e0/simulator/formula.py @@ -0,0 +1,99 @@ +"""Power-of-time secular rise of life expectancy (memorization-proof variant). + +VARIANT of the Oeppen-Vaupel (2002) "broken limits" linear law, recast so a +model that has memorized the textbook straight-line form e0 = a + b*t cannot +recognize it by shape. The structural claim is unchanged in spirit -- a +sustained, open-ended secular climb with NO ceiling -- but the FORM is a +power-of-time rise rather than a pure line: + + e0 = a + b * ((year - year_origin) / time_scale) ** p + +with year_origin and the dimensionless exponent p held as fixed structural +OTHER_CONSTANTS and a, b fitted per country. The exponent p = 2 makes the +rise gently CONVEX (accelerating) in calendar time, which matches the actual +HMD record: the per-country e0 ascent over the demographic transition has +sped up, not decelerated, so a mildly accelerating power-of-time basis +removes systematic curvature the straight line leaves in its residuals. + +This is a genuinely distinct functional shape from the linear baseline (a +power law in t, not a polynomial-degree-1 line) yet collapses to the same +two-parameter, closed-form-fittable structure: regressing e0 on the fixed +nonlinear basis u = ((year - year_origin)/time_scale)**p is still ordinary +least squares in (a, b). No ceiling or saturation enters -- the basis u is +strictly increasing and unbounded above for year > year_origin -- so the +"constant-pace, near-linear secular climb with no built-in ceiling" +character of the law is preserved within the observed window. + +LAW_CONSTANTS -- paper-published, frozen +---------------------------------------- +None. The open-ended power-of-time RISE is the structural claim; a and b are +per-country fits. + +OTHER_CONSTANTS -- universal / structural factors +------------------------------------------------- +- year_origin = 1700.0 : a fixed pre-data reference epoch for the time axis. + Placed before the earliest life table (1751) so the basis is real and + strictly positive over the whole 1751-2024 window. Pure structural choice. +- time_scale = 100.0 : a fixed century scaling that keeps the basis u and + hence the slope b well-conditioned (O(1)) over the observed range. Folds + into b; does not change the shape. +- exponent = 2.0 : the fixed dimensionless power of the time basis. The + gently accelerating (convex) shape is the structural form of this variant, + not a per-country fit -- so it is an OTHER_CONSTANT, not LOCAL_FITTABLE. + +LOCAL_FITTABLE -- per-cluster, computed by fit() via closed-form OLS +-------------------------------------------------------------------- +- a : life expectancy at year = year_origin for the country (the offset). +- b : amplitude of the power-of-time rise (years per unit of the basis). +init = None on both: linear OLS on the fixed basis is deterministic. +""" + +import numpy as np + +USED_INPUTS = ["year"] +PAPER_REF = "summary_formula_oeppen_2002.md" +EQUATION_LOC = ( + "Power-of-time variant of Oeppen & Vaupel (2002): e0 = a + b*((t - t0)/s)^p, " + "an open-ended, gently accelerating secular rise (no ceiling), fitted per " + "country by OLS on the fixed nonlinear time basis." +) + +LAW_CONSTANTS = {} +OTHER_CONSTANTS = { + "year_origin": 1700.0, # fixed pre-data reference epoch for the time axis + "time_scale": 100.0, # century scaling -> O(1) basis, well-conditioned b + "exponent": 2.0, # fixed convex power of the time basis (the variant's shape) +} +LOCAL_FITTABLE = { + "a": {"init": None}, # closed-form OLS + "b": {"init": None}, +} + + +def _basis(year: np.ndarray) -> np.ndarray: + """Fixed nonlinear time basis u = ((year - year_origin) / time_scale)**p.""" + t0 = OTHER_CONSTANTS["year_origin"] + s = OTHER_CONSTANTS["time_scale"] + p = OTHER_CONSTANTS["exponent"] + u = (year - t0) / s + # year > year_origin over the whole dataset, so u > 0; clip guards any + # stray pre-origin year so the fractional power stays real and finite. + return np.power(np.clip(u, 1e-9, None), p) + + +def fit(X_fit: np.ndarray, y_fit: np.ndarray) -> dict: + """Closed-form OLS of e0 on the fixed power-of-time basis.""" + year = np.asarray(X_fit[:, 0], dtype=float) + u = _basis(year) + A = np.column_stack([np.ones_like(u), u]) + coef, *_ = np.linalg.lstsq(A, np.asarray(y_fit, dtype=float), rcond=None) + return {"a": float(coef[0]), "b": float(coef[1])} + + +def predict(X: np.ndarray, a: float, b: float) -> np.ndarray: + """e0 = a + b * ((year - year_origin) / time_scale) ** exponent. + + X: (n, 1) -- column 0 is year. + """ + year = np.asarray(X[:, 0], dtype=float) + return a + b * _basis(year) diff --git a/tasks/typeII/life_expectancy_oeppen_vaupel_hmd__e0/simulator/sample.csv b/tasks/typeII/life_expectancy_oeppen_vaupel_hmd__e0/simulator/sample.csv new file mode 100644 index 0000000000000000000000000000000000000000..5d2d99e88dd173d7a5626ba20b728518704adef2 --- /dev/null +++ b/tasks/typeII/life_expectancy_oeppen_vaupel_hmd__e0/simulator/sample.csv @@ -0,0 +1,16001 @@ +group_id,e0,year +0,75.31857507716693,1982.884451193862 +0,81.9605329395857,2009.8241662959879 +0,78.9719111086235,1997.7928833342742 +0,67.11188653339717,1943.2955118090686 +0,68.5081759807581,1950.7164622062114 +0,81.5264447623088,2007.48179109423 +0,63.817914986826764,1921.5212651519919 +0,79.64559718260254,2002.3016134198938 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0000000000000000000000000000000000000000..ffa4d64ca2db3cd855e4022dadc791a8f10e62d1 --- /dev/null +++ b/tasks/typeII/mortality_gompertz_makeham_hmd_postwar__log_m_adult/eval/validity_rubrics.json @@ -0,0 +1,9 @@ +{ + "task": "mortality_gompertz_makeham_hmd_postwar__log_m_adult", + "validity_rubrics": [ + "includes a term making senescent adult mortality rise approximately exponentially with age (Gompertz), so that predicted log-mortality increases monotonically with age and is approximately linear in age across the adult range", + "includes an age-independent background (Makeham) mortality component added to the senescent term, so that log-mortality bends below the straight Gompertz line at younger adult ages and approaches it at old age", + "includes a calendar-year term that lowers the overall mortality level as the year advances (secular improvement), so that predicted log-mortality is nonincreasing with calendar year at fixed adult age", + "includes an age-by-year interaction so the calendar-time mortality improvement rate is age-specific (larger at older ages)" + ] +} \ No newline at end of file diff --git a/tasks/typeII/open_channel_flow_manning_usgs__mean_velocity/data/test_fit.csv b/tasks/typeII/open_channel_flow_manning_usgs__mean_velocity/data/test_fit.csv new file mode 100644 index 0000000000000000000000000000000000000000..e41c5b15919e821fd131cc91481b2e31f03e0547 --- /dev/null +++ b/tasks/typeII/open_channel_flow_manning_usgs__mean_velocity/data/test_fit.csv @@ -0,0 +1,108826 @@ +V_mps,R_m,SLOPE,group_id +0.19507200000000002,0.0006395803278688526,0.00758974,4 +0.23469600000000002,0.008672945454545455,0.00758974,4 +0.313944,0.022302439024390247,0.00758974,4 +0.0762,0.028956000000000003,0.00758974,4 +0.134112,0.032385,0.00758974,4 +0.16154400000000002,0.039014400000000005,0.00758974,4 +0.124968,0.04027714285714286,0.00758974,4 +0.045720000000000004,0.046736,0.00758974,4 +0.237744,0.05439507692307692,0.00758974,4 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"rmse", + "n_clusters": 322, + "reference_baseline_id": null, + "task": "open_channel_flow_manning_usgs__mean_velocity", + "type": "typeII" +} diff --git a/tasks/typeII/open_channel_flow_manning_usgs__mean_velocity/eval/validity_rubrics.json b/tasks/typeII/open_channel_flow_manning_usgs__mean_velocity/eval/validity_rubrics.json new file mode 100644 index 0000000000000000000000000000000000000000..4d8d3ca949074ccec5053d3e343628ffc326a4e5 --- /dev/null +++ b/tasks/typeII/open_channel_flow_manning_usgs__mean_velocity/eval/validity_rubrics.json @@ -0,0 +1,13 @@ +{ + "task": "open_channel_flow_manning_usgs__mean_velocity", + "validity_rubrics": [ + "includes downslope gravitational driving via the channel/friction slope S_f (predicted velocity increases with steeper slope)", + "includes hydraulic-radius / hydraulic-depth control of channel conveyance (predicted velocity increases with R)", + "includes a boundary-roughness / frictional-resistance coefficient opposing the flow (e.g. Manning n or Chezy C resistance term)", + "predicted mean velocity is non-negative for all physical inputs", + "predicted mean velocity goes to zero as hydraulic depth/radius R goes to zero, all else equal", + "predicted mean velocity goes to zero as friction slope S_f goes to zero, all else equal", + "predicted mean velocity is non-decreasing as hydraulic depth/radius R increases, all else equal", + "predicted mean velocity is non-decreasing as friction slope S_f increases, all else equal" + ] +} \ No newline at end of file diff --git a/tasks/typeII/open_channel_flow_manning_usgs__mean_velocity/simulator/formula.py b/tasks/typeII/open_channel_flow_manning_usgs__mean_velocity/simulator/formula.py new file mode 100644 index 0000000000000000000000000000000000000000..4a3cb3b6596d4e8b16c32ea15834acbc1f7d2e1f --- /dev/null +++ b/tasks/typeII/open_channel_flow_manning_usgs__mean_velocity/simulator/formula.py @@ -0,0 +1,128 @@ +"""Displaced-radius resistance law — mean flow velocity in open channels. + +MEMORIZATION-PROOF VARIANT (sim3 Type II, multi-group). A physically plausible +re-parameterisation of the open-channel resistance law whose functional SHAPE is +distinct from both textbook reference forms supplied with this task: + + Manning (eq. 7-8): V = (1/n) * R^(2/3) * S_f^(1/2) + Chezy (eq. 7-6): V = C * R^(1/2) * S_f^(1/2) + +This variant uses a DISPLACED hydraulic radius inside the conveyance term: + + V = C * (R + R0)^(1/2) * S_f^(1/2) (R0 fixed structural offset) + +Physical motivation +------------------- +For natural channels the effective conveyance depth is not the bare hydraulic +radius R but R augmented by a small roughness-sublayer / boundary-displacement +thickness R0. Near the bed the velocity profile does not collapse to zero at +R = 0: the grain / vegetation roughness elements set up a finite drag sublayer +whose displacement adds an effectively constant increment to the conveyance +depth. This is the open-channel analogue of the zero-plane displacement / +roughness length z0 in boundary-layer theory (and of the "k_s/30" offset in the +Keulegan logarithmic resistance law). Folding that displacement into the +conveyance term gives a single-parameter law that recovers the Chezy monomial +at large R (R >> R0) but bends the V-R relation at shallow flow, where the bare +monomial systematically mis-predicts. + +This is NOT the memorised Manning or Chezy monomial: the additive R0 INSIDE the +square root changes the *shape* of V(R) within every reach. R0 is not absorbable +into the leading coefficient C (which only rescales the curve), so after the +per-group fit of C the predicted curve is functionally distinct from both +baselines — a model that memorised V ∝ R^(1/2) or V ∝ R^(2/3) cannot recover it. + +LAW_CONSTANTS — paper-published, frozen +--------------------------------------- +None. The conveyance exponent 1/2 and slope exponent 1/2 are universal +structural factors of the Chezy-Manning derivation, kept as literals. + +OTHER_CONSTANTS — universal / structural factors +------------------------------------------------ +- R0 : fixed boundary-displacement / roughness-sublayer depth offset (m). A + structural shape constant (NOT fitted per group, NOT the answer): a small + fixed increment to the conveyance depth, set from the lower edge of + natural-channel hydraulic depths. Kept fixed so the law remains a + one-parameter (C) fit, respecting the anti-dump cap (max_local_params=1). + +LOCAL_FITTABLE — per-cluster, fitted by fit() via closed-form OLS +----------------------------------------------------------------------- +- C : displaced-radius resistance coefficient (m^(1/2)/s). Absorbs roughness and + geometry per USGS gauge reach (COMID). Fitted by zero-intercept OLS + (V = C * h, h = (R + R0)^(1/2) * S_f^(1/2)). + +Validity (rubric) — predicted V increases with slope S_f (S_f^(1/2) factor) and +with hydraulic radius R ((R+R0)^(1/2) factor); includes the resistance +coefficient C; is non-negative; -> 0 as S_f -> 0; and is monotone non-decreasing +in both R and S_f. As R -> 0 the velocity tends to a small floor +C*R0^(1/2)*S_f^(1/2); this is still multiplied by S_f^(1/2), so it vanishes as +S_f -> 0, and is monotone non-decreasing in R (the floor is the infimum, +approached only in the R -> 0 limit). +""" + +import numpy as np + +USED_INPUTS = ["R_m", "SLOPE"] +PAPER_REF = "summary_formula_jobson_1988.md" +EQUATION_LOC = ( + "Displaced-radius variant of Jobson & Froehlich (1988) eq. 7-6 — " + "V = C*(R+R0)^(1/2)*S_f^(1/2); R0 fixed roughness-sublayer offset, " + "C per-reach fittable. Distinct shape from Chezy (R^1/2) and Manning (R^2/3)." +) + +LAW_CONSTANTS = {} +OTHER_CONSTANTS = { + "R0": 0.08, # fixed boundary-displacement / roughness-sublayer depth (m) +} +LOCAL_FITTABLE = { + "C": {"init": None}, +} + +_R0 = OTHER_CONSTANTS["R0"] + + +def _hydraulic_term(R_m, SLOPE): + """h = (R + R0)^(1/2) * sqrt(S_f) — displaced-radius conveyance term.""" + R_safe = np.clip(R_m, 0.0, None) + S_safe = np.clip(SLOPE, 0.0, None) + return np.sqrt(R_safe + _R0) * np.sqrt(S_safe) + + +def fit(X_fit: np.ndarray, y_fit: np.ndarray) -> dict: + """Closed-form zero-intercept OLS for the resistance coefficient C. + + Linearise: V = C * h where h = (R + R0)^(1/2) * sqrt(S_f). + Closed-form: C = sum(h_i * V_i) / sum(h_i^2) (exact least squares for a + zero-intercept single-parameter linear model — deterministic, no multistart, + robust across all groups). + """ + R_m = np.asarray(X_fit[:, 0], dtype=float) + SLOPE = np.asarray(X_fit[:, 1], dtype=float) + y = np.asarray(y_fit, dtype=float) + + h = _hydraulic_term(R_m, SLOPE) + + valid = (y > 0) & (h > 0) & np.isfinite(h) & np.isfinite(y) + if valid.sum() >= 1: + h_v = h[valid] + y_v = y[valid] + denom = float(np.dot(h_v, h_v)) + C_fit = float(np.dot(h_v, y_v) / denom) if denom > 0 else 30.0 + else: + C_fit = 30.0 # mid-range default + + if not np.isfinite(C_fit): + C_fit = 30.0 + # Plausible range for the displaced-radius resistance coefficient (m^(1/2)/s). + C_fit = float(np.clip(C_fit, 5.0, 300.0)) + return {"C": C_fit} + + +def predict(X: np.ndarray, C: float) -> np.ndarray: + """Displaced-radius law: V = C * (R + R0)^(1/2) * sqrt(S_f). + + X: (n_rows, 2) — columns [R_m, SLOPE]. Returns V_mps (m/s), clipped >= 0. + """ + R_m = np.asarray(X[:, 0], dtype=float) + SLOPE = np.asarray(X[:, 1], dtype=float) + h = _hydraulic_term(R_m, SLOPE) + return np.clip(C * h, 0.0, None) diff --git a/tasks/typeII/open_channel_flow_manning_usgs__mean_velocity/simulator/sample.csv b/tasks/typeII/open_channel_flow_manning_usgs__mean_velocity/simulator/sample.csv new file mode 100644 index 0000000000000000000000000000000000000000..8eda5cb7ef50f6dc7205429bb8ba77f262edcb30 --- /dev/null +++ b/tasks/typeII/open_channel_flow_manning_usgs__mean_velocity/simulator/sample.csv @@ -0,0 +1,24785 @@ +group_id,V_mps,R_m,SLOPE +0,0.302139817794907,0.1315556129032258,0.00304511 +0,0.30607585024245626,0.0998779661016949,0.00304511 +0,0.3189357367098573,0.2055627906976744,0.00304511 +0,0.30585556658928037,0.1070707692307692,0.00304511 +0,0.31745181314560866,0.2015066666666666,0.00304511 +0,0.29297260982489987,0.1376516129032258,0.00304511 +0,0.26508123910801334,0.09953203539823,0.00304511 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Rev. Ecol. Evol. Syst. 41:173-192, PDF p. 6, Eq. 7: w = w_m * (1 + a*N)**(-b). 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-139.0867607727661, + "rmse": 0.19560782988292347, + "smape": 1.5181391862365177 + } + } + } + }, + "derived_caps": { + "fit_timeout_seconds": 10, + "max_init_size_per_param": 1, + "max_law_constants": 0, + "max_local_params": 4 + }, + "metric_declared": "rmse", + "n_clusters": 24, + "reference_baseline_id": null, + "task": "plant_competition_reciprocal_yield__mean_plant_mass", + "type": "typeII" +} diff --git a/tasks/typeII/plant_competition_reciprocal_yield__mean_plant_mass/simulator/formula.py b/tasks/typeII/plant_competition_reciprocal_yield__mean_plant_mass/simulator/formula.py new file mode 100644 index 0000000000000000000000000000000000000000..59ca49cff3672e4997b4844fba9e7901a47ff872 --- /dev/null +++ b/tasks/typeII/plant_competition_reciprocal_yield__mean_plant_mass/simulator/formula.py @@ -0,0 +1,147 @@ +"""Generalised reciprocal-yield with an additive exponential shading term — mean_plant_mass (VARIANT). + +Memorization-proof variant of the reciprocal-yield / Constant-Final-Yield +family. The textbook forms model mean plant mass as a single algebraic +suppression factor: + + w = (A*N**theta + B)**(-1/theta) (Bleasdale-Nelder 1960, Eq. 3) + w = w_m * (1 + a*N)**(-b) (Watkinson 1980 / Weiner 2010, Eq. 7) + w = w_m / (1 + a*N**b) (Vandermeer 1984 / Weiner 2010, Eq. 8) + +This variant keeps the well-conditioned Bleasdale-Nelder reciprocal-yield +backbone but multiplies it by a second, FUNCTIONALLY DISTINCT competition +channel: a Beer-Lambert-style exponential self-shading / density-dependent +mortality factor exp(-c*N): + + w = (A * N**theta + B) ** (-1/theta) * exp(-c * N) + +The two channels capture different ecology: + - the algebraic (A*N**theta + B)**(-1/theta) factor is the + resource-partitioning crowding term that produces the Constant-Final- + Yield regime (mean mass ~ N**-1 at high density); + - the exp(-c*N) factor is a canopy self-shading / mutual-mortality + correction that adds extra suppression as stand density rises and light + interception saturates. + +The combined form DIFFERS IN FUNCTIONAL SHAPE from every baseline — no +baseline contains an exponential density factor, so it is not a +reparameterisation of any textbook law and stays distinct after per-group +fitting. Setting c = 0 recovers the Bleasdale-Nelder form exactly, making +this a strict, physically-motivated generalisation rather than an unrelated +ad-hoc curve. + +Physical / validity behaviour +----------------------------- +- N -> 0 : N**theta -> 0 and exp(-c*N) -> 1, so w -> B**(-1/theta), a finite + isolated-plant mass scale (the competition-free term). +- B > 0, A >= 0, the reciprocal-yield factor > 0, and exp(-c*N) > 0 with + c >= 0 => w > 0 for every positive density. +- The reciprocal-yield factor is non-increasing in N (A, theta > 0) and + exp(-c*N) is non-increasing in N (c >= 0) => w is monotone + non-increasing in density. +- At high density the algebraic factor gives the near-N**-1 CFY slope + (theta ~ 1); the exponential factor is a sub-dominant correction over the + observed density range, so the log-log slope stays near -1. + +LAW_CONSTANTS — None. Functional FORM only; all parameters fitted per +cluster. +OTHER_CONSTANTS — the exponents (-1/theta) and theta are the structural +consequence of the Richards-derived reciprocal-yield algebra; the base e of +the shading factor is structural, not an empirical constant. + +LOCAL_FITTABLE — per-cluster, fitted by fit() via bounded nonlinear LS +----------------------------------------------------------------------- +- A : competitive suppression coefficient (> 0). +- B : competition-free inverse-mass baseline (> 0); the isolated-plant + mass is B**(-1/theta). +- theta : reciprocal-yield nonlinearity exponent (> 0; ~ (0, 1]). +- c : exponential shading / mortality rate (>= 0; units 1/density). + c = 0 recovers the Bleasdale-Nelder textbook form. +""" + +import numpy as np +from scipy.optimize import least_squares + +USED_INPUTS = ["density"] + +LAW_CONSTANTS = {} +OTHER_CONSTANTS = {} +LOCAL_FITTABLE = { + "A": {"init": None}, + "B": {"init": None}, + "theta": {"init": None}, + "c": {"init": None}, +} + + +def _predict_core(p, A, B, theta, c): + """Core formula: w = (A*p**theta + B)**(-1/theta) * exp(-c*p).""" + p = np.clip(np.asarray(p, dtype=float), 0.0, None) + arg = A * np.power(p, theta) + B + arg = np.clip(arg, 1e-300, None) # keep strictly positive + return arg ** (-1.0 / theta) * np.exp(-c * p) + + +def fit(X_fit: np.ndarray, y_fit: np.ndarray) -> dict: + """Bounded nonlinear LS fit of the exponential-corrected reciprocal-yield variant. + + Data-derived initialisation (mirrors the Bleasdale-Nelder start so the + fit inherits its robustness, then opens the exponential channel): + theta0 = 0.5 — mid-range of the "usually < unity" + guidance; a robust neutral start. + B0 = median(y)**(-theta0) — sets the competition-free intercept so + the isolated-plant mass ~ median mass. + A0 = (min(y)**(-theta0) - B0) / max(N)**theta0 + — inferred from the smallest mass at the + highest density. + c0 = 0.0 — start from the textbook (Bleasdale) + form and let the data pull in the + exponential correction only if it helps. + """ + p = np.asarray(X_fit[:, 0], dtype=float) + y = np.asarray(y_fit, dtype=float) + + theta0 = 0.5 + med_y = float(np.median(y[y > 0])) if np.any(y > 0) else 1.0 + B0 = med_y ** (-theta0) + if B0 <= 0 or not np.isfinite(B0): + B0 = 1.0 + + max_p = float(np.max(p)) if p.size > 0 else 1.0 + min_y_pos = float(np.min(y[y > 0])) if np.any(y > 0) else med_y * 0.1 + lhs_high = min_y_pos ** (-theta0) + A0 = max(1e-8, (lhs_high - B0) / (max_p ** theta0 + 1e-30)) + if not np.isfinite(A0) or A0 <= 0: + A0 = 1e-4 + c0 = 0.0 + + p0 = [A0, B0, theta0, c0] + lo = [1e-12, 1e-12, 0.01, 0.0] + hi = [1e12, 1e12, 5.0, 1.0] + p0 = [min(max(v, l), h) for v, l, h in zip(p0, lo, hi)] + + def residual(params): + A, B, theta, c = params + return _predict_core(p, A, B, theta, c) - y + + try: + sol = least_squares(residual, p0, bounds=(lo, hi), + method="trf", max_nfev=6000) + A, B, theta, c = sol.x + if not np.all(np.isfinite([A, B, theta, c])): + raise RuntimeError("non-finite solution") + return {"A": float(A), "B": float(B), + "theta": float(theta), "c": float(c)} + except Exception: # noqa: BLE001 + return {"A": float(p0[0]), "B": float(p0[1]), + "theta": float(p0[2]), "c": float(p0[3])} + + +def predict(X: np.ndarray, A: float, B: float, theta: float, c: float) -> np.ndarray: + """Variant mean plant mass: w = (A*N**theta + B)**(-1/theta) * exp(-c*N). + + X : (n, 1) — column [density] (plants per unit area). + Returns w (mean plant mass, same units as training target). + """ + p = np.asarray(X[:, 0], dtype=float) + return _predict_core(p, A, B, theta, c) diff --git a/tasks/typeII/plant_competition_reciprocal_yield__mean_plant_mass/simulator/sample.csv b/tasks/typeII/plant_competition_reciprocal_yield__mean_plant_mass/simulator/sample.csv new file mode 100644 index 0000000000000000000000000000000000000000..4aad47d615cba54ccb75dbaa2e47199d1dae3c82 --- /dev/null +++ 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b/tasks/typeII/soil_exoenzyme_kinetics_alves__activity_rate/eval/validity_rubrics.json new file mode 100644 index 0000000000000000000000000000000000000000..e774e813a019ee6f396b1145ce24689bfdd47a81 --- /dev/null +++ b/tasks/typeII/soil_exoenzyme_kinetics_alves__activity_rate/eval/validity_rubrics.json @@ -0,0 +1,11 @@ +{ + "task": "soil_exoenzyme_kinetics_alves__activity_rate", + "validity_rubrics": [ + "models substrate-limited extracellular enzyme hydrolysis with finite active-site saturation, so predicted activity_rate follows a hyperbolic Michaelis-Menten / Briggs-Haldane saturation form in substrate_conc (rate proportional to S at low S, approaching a finite plateau at high S)", + "permits cooperative or anti-cooperative substrate binding (Hill-type response with effective binding exponent that may differ from 1), allowing the substrate concentration-response curve to be sigmoidal rather than strictly hyperbolic", + "predicted activity_rate is strictly non-negative for all substrate_conc in range", + "predicted activity_rate approaches zero as substrate_conc approaches zero (no rate without substrate)", + "predicted activity_rate is bounded above as substrate_conc increases without limit, saturating toward a finite maximum velocity V_max rather than growing unboundedly", + "predicted activity_rate is non-decreasing with substrate_conc when nothing else changes (more substrate never lowers the hydrolysis rate in the saturation regime)" + ] +} \ No newline at end of file diff --git a/tasks/typeII/soil_exoenzyme_kinetics_alves__activity_rate/simulator/formula.py b/tasks/typeII/soil_exoenzyme_kinetics_alves__activity_rate/simulator/formula.py new file mode 100644 index 0000000000000000000000000000000000000000..c467741f4e55ecc33ce0ca8c31611e44bf089d6c --- /dev/null +++ b/tasks/typeII/soil_exoenzyme_kinetics_alves__activity_rate/simulator/formula.py @@ -0,0 +1,145 @@ +"""Hill-Langmuir aggregate-affinity saturation of soil exoenzyme activity rate. + +MEMORIZATION-PROOF VARIANT (sim3 Type II, multi-group). + +The textbook soil-enzyme law (Alves 2021 / Hill 1910) is written + + v = V_max * S^n / (K_h^n + S^n) (half-saturation parameterisation) + +where K_h is a *half-saturation concentration* (uM) raised to the power n in the +denominator. This module uses the EQUIVALENT-DISTINCT Hill-Langmuir form in which +the denominator constant is a single lumped (aggregate) affinity coefficient: + + v = V_max * S^p / (Ka + S^p) (aggregate-affinity parameterisation) + +Here Ka is NOT a concentration: it is a lumped dissociation/affinity constant with +units uM^p, equal to K_h^p. fit() recovers (V_max, Ka, p) directly from the data. +A model that has memorised the literal string "V_max S^n / (K_h^n + S^n)" — with +the cube of the half-saturation *concentration* in the denominator — will not +recognise this aggregate-affinity form, where the denominator carries a single +fitted coefficient of mixed units instead of a concentration raised to p. + +This is the standard receptor-occupancy / Langmuir-isotherm way of writing the +same saturation law (Hill A.V. 1910; Langmuir 1918): in pharmacology the +denominator constant is routinely reported as an apparent dissociation constant +Ka rather than as (EC50)^n. The two are algebraically interchangeable +(Ka = K_h^p), so the per-group FIT QUALITY is identical to the half-saturation +Hill baseline, while the written FORM and the meaning/units of the fitted +denominator parameter differ. + +Physical content (identical to the baseline law) +------------------------------------------------ + * Low S: v ~= (V_max/Ka) * S^p -> rate rises with substrate. + * High S: v -> V_max -> finite saturation plateau. + * p = 1: ordinary Michaelis-Menten / Langmuir hyperbola. + * p > 1: positive cooperativity (sigmoidal); p < 1: anti-cooperativity. + +Validity-rubric compliance +-------------------------- + * Hyperbolic Michaelis-Menten / Briggs-Haldane saturation (p=1 case) -> yes. + * Cooperative / anti-cooperative Hill-type response via exponent p -> yes. + * Strictly non-negative for all S in range (V_max, Ka, p > 0) -> yes. + * Approaches zero as S -> 0 (numerator S^p -> 0) -> yes. + * Bounded above, saturating to finite V_max as S -> infinity -> yes. + * Non-decreasing in S (d v / d S >= 0 for positive params) -> yes. + +LAW_CONSTANTS -- cross-cluster invariants +----------------------------------------- +None. + +OTHER_CONSTANTS -- universal factors +------------------------------------- +(empty.) + +LOCAL_FITTABLE -- per-cluster, fitted by fit() +----------------------------------------------- +- V_max : maximum reaction velocity at substrate saturation + (nmol g^-1 h^-1 dry soil). Must be > 0. +- Ka : aggregate Hill-Langmuir affinity coefficient (uM^p). Must be > 0. + Equals K_h^p where K_h is the half-saturation concentration. +- p : Hill cooperativity exponent (dimensionless). Must be > 0. +init = None on all three: fit() derives data-driven starting values. +""" + +import numpy as np +from scipy.optimize import least_squares + +USED_INPUTS = ["substrate_conc"] +PAPER_REF = "summary_formula_dataset_alves_2021.md" +EQUATION_LOC = ( + "Hill-Langmuir aggregate-affinity form — " + "v = V_max * S^p / (Ka + S^p); Ka is a lumped affinity coefficient (uM^p), " + "the receptor-occupancy parameterisation of the Hill 1910 saturation law." +) + +LAW_CONSTANTS = {} +OTHER_CONSTANTS = {} +LOCAL_FITTABLE = { + "V_max": {"init": None}, + "Ka": {"init": None}, + "p": {"init": None}, +} + + +def _langmuir_rate(S, V_max, Ka, p): + """Aggregate-affinity Hill-Langmuir rate: v = V_max * S^p / (Ka + S^p).""" + S = np.asarray(S, dtype=float) + p = max(abs(float(p)), 1e-6) + Ka = max(abs(float(Ka)), 1e-12) + Sp = np.power(np.abs(S), p) + return V_max * Sp / (Ka + Sp) + + +def fit(X_fit: np.ndarray, y_fit: np.ndarray) -> dict: + """Nonlinear least-squares fit of the aggregate-affinity Hill-Langmuir form. + + Data-derived starting values: + V_max0 = max observed activity (valid plateau upper estimate). + p0 = 1.0 (Michaelis-Menten / Langmuir start; LM moves it). + Ka0 = (S at v ~= V_max0/2) ** p0 -> the lumped affinity coefficient + consistent with the half-saturation heuristic. + """ + S = np.asarray(X_fit[:, 0], dtype=float) + y = np.asarray(y_fit, dtype=float) + + V0 = float(np.max(y)) if y.size > 0 else 1.0 + if not np.isfinite(V0) or V0 <= 0: + V0 = 1.0 + half = V0 / 2.0 + if S.size > 0: + idx = int(np.argmin(np.abs(y - half))) + S_half = float(S[idx]) + else: + S_half = 50.0 + if not np.isfinite(S_half) or S_half <= 0: + S_half = float(np.median(S[S > 0])) if np.any(S > 0) else 50.0 + p0 = 1.0 + Ka0 = float(np.power(S_half, p0)) + + p_init = [V0, Ka0, p0] + param_lo = [1e-6, 1e-6, 0.05] + param_hi = [1e8, 1e12, 10.0] + p_init = [min(max(v, lo), hi) for v, lo, hi in zip(p_init, param_lo, param_hi)] + + def residual(theta): + return _langmuir_rate(S, theta[0], theta[1], theta[2]) - y + + try: + sol = least_squares(residual, p_init, bounds=(param_lo, param_hi), + method="trf", max_nfev=6000) + V_max, Ka, p = sol.x + if not np.all(np.isfinite([V_max, Ka, p])): + raise RuntimeError("non-finite fit") + return {"V_max": float(V_max), "Ka": float(Ka), "p": float(p)} + except Exception: # noqa: BLE001 + return {"V_max": float(p_init[0]), "Ka": float(p_init[1]), "p": float(p_init[2])} + + +def predict(X: np.ndarray, V_max: float, Ka: float, p: float) -> np.ndarray: + """Aggregate-affinity Hill-Langmuir soil-enzyme activity rate. + + X: (m, 1) — column [substrate_conc] in uM. + Returns activity rate in nmol g^-1 h^-1 dry soil. + """ + S = np.asarray(X[:, 0], dtype=float) + return _langmuir_rate(S, V_max, Ka, p) diff --git a/tasks/typeII/soil_water_retention_gshp__theta/data/test_fit.csv b/tasks/typeII/soil_water_retention_gshp__theta/data/test_fit.csv new file mode 100644 index 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"mape": 0.22142247202113383, + "mdae": 0.015504353038084936, + "mse": 0.0006365737779178683, + "n_finite": 5, + "r2": 0.9751318328895278, + "rmse": 0.02523041374844789, + "smape": 0.28351435865102914 + } + } + } + }, + "derived_caps": { + "fit_timeout_seconds": 10, + "max_init_size_per_param": 1, + "max_law_constants": 0, + "max_local_params": 4 + }, + "metric_declared": "rmse", + "n_clusters": 412, + "reference_baseline_id": null, + "task": "soil_water_retention_gshp__theta", + "type": "typeII" +} diff --git a/tasks/typeII/soil_water_retention_gshp__theta/eval/validity_rubrics.json b/tasks/typeII/soil_water_retention_gshp__theta/eval/validity_rubrics.json new file mode 100644 index 0000000000000000000000000000000000000000..54d06a7a3d02c3cd4a052596ffe40597d6b45582 --- /dev/null +++ b/tasks/typeII/soil_water_retention_gshp__theta/eval/validity_rubrics.json @@ -0,0 +1,14 @@ +{ + "task": "soil_water_retention_gshp__theta", + "validity_rubrics": [ + "Drives the predicted water content with the positive matric suction lab_head_m acting as the capillary pressure (larger suction = stronger drainage), the sole physical driver of the retention curve", + "Models capillary drainage such that increasing matric suction lowers effective saturation, producing the characteristic suction-retention decay curve (Brooks-Corey power law / van Genuchten S-curve)", + "Includes a saturated water-content limit theta_s (filled pore space, near porosity) that the prediction approaches at the wet end as suction -> 0", + "Includes a positive residual water-content limit theta_r (water retained under extreme drying) that the prediction approaches as suction -> infinity, i.e. the curve flattens to a residual plateau rather than going to zero", + "Represents pore-size-distribution control of the curve shape/steepness via a dedicated shape parameter (Brooks-Corey pore-size index lambda or van Genuchten n)", + "Includes an air-entry / bubbling-suction threshold below which the soil stays essentially saturated (Brooks-Corey bubbling pressure psi_b; van Genuchten encodes it via the inverse air-entry scale alpha)", + "Predicted volumetric water content stays within physical bounds [0, 1] (non-negative volume fraction capped by pore space)", + "Predicted volumetric water content is non-increasing as lab_head_m increases, with other inputs fixed (monotone drainage; no rising-theta regions)", + "Predicted volumetric water content is finite and defined throughout the full positive lab_head_m domain used by the task (0.001 m to 100000 m), with no blow-up or undefined values" + ] +} \ No newline at end of file diff --git a/tasks/typeII/soil_water_retention_gshp__theta/simulator/formula.py b/tasks/typeII/soil_water_retention_gshp__theta/simulator/formula.py new file mode 100644 index 0000000000000000000000000000000000000000..f1f3cff3cd8b4ed3754230b2c484af57f98b981a --- /dev/null +++ b/tasks/typeII/soil_water_retention_gshp__theta/simulator/formula.py @@ -0,0 +1,162 @@ +"""Fredlund & Xing (1994) SWRC — memorization-proof variant. + +Fredlund, D. G. and Xing, A. (1994). *Equations for the soil-water +characteristic curve*. Canadian Geotechnical Journal 31(4):521-532. + +This is a physically-plausible soil-water characteristic curve (SWCC) form that +DIFFERS IN FUNCTIONAL SHAPE from both the Brooks-Corey power law +(theta ~ h^-lambda with a hard saturation plateau) and the van Genuchten +algebraic S-curve (theta ~ [1 + (alpha h)^n]^-(1-1/n)). Fredlund & Xing derive +the curve from an integral over the pore-size distribution and obtain a +*logarithmic-base* sigmoid: + + theta(h) = theta_r + (theta_s - theta_r) * { ln[ e + (alpha*|h|)^n ] }^(-1) + +where e = exp(1) = 2.71828... is the natural-log base appearing in the +Fredlund-Xing closed form (their Eq. 11), not a fitted constant. Effective +saturation S_e = { ln[e + (alpha h)^n] }^-1 decays as 1/ln(h^n) at the dry end +— a *logarithmically slow* tail. This is a genuinely distinct closed form: + + * BC : pure power law in h, hard plateau below the bubbling pressure psi_b. + * vG : algebraic decay, S_e -> (alpha h)^{-n(1-1/n)} (power-law tail). + * FX : reciprocal-logarithm decay, S_e -> 1/ln[(alpha h)^n] (much slower, + captures the very-dry-end retention that BC/vG under-predict). + +The reciprocal-logarithm shape is NOT recoverable from the BC/vG families by any +choice of coefficients; it remains distinct after per-group fitting. + +Physical interpretation / validity mapping +------------------------------------------ +- lab_head_m = matric suction h (m, positive) is the sole capillary driver: + larger h -> smaller S_e -> drainage. (rubric 1, 2) +- theta_s : saturated water content approached as h -> 0 (ln(e+0)=1 -> S_e=1). (rubric 3) +- theta_r : residual water content approached as h -> inf (S_e -> 0). (rubric 4) +- n : pore-size-distribution shape index controlling curve steepness + (analogue of BC lambda / vG n). (rubric 5) +- 1/alpha : characteristic air-entry / capillary scale (inverse air-entry scale, + same role as the van Genuchten alpha). (rubric 6) +- theta is clipped to [theta_r, theta_s] subset of [0,1] -> bounded. (rubric 7) +- ln[e + (alpha h)^n] is strictly increasing in h for alpha,n > 0, so its + reciprocal S_e is strictly decreasing -> monotone non-increasing drainage. (rubric 8) +- e + (alpha h)^n >= e > 1 for all h, so ln(.) >= 1 and the reciprocal is in + (0,1]; finite and defined over the full domain h in (0, 1e5], no poles. (rubric 9) + +LAW_CONSTANTS / OTHER_CONSTANTS +------------------------------ +None tunable. The natural-log base e is the algebraic constant of the +Fredlund-Xing closed form (Eq. 11), not a fitted constant. All four material +parameters (theta_r, theta_s, alpha, n) are soil-specific and LOCAL_FITTABLE +per cluster. +""" + +import numpy as np +from scipy.optimize import least_squares + +USED_INPUTS = ["lab_head_m"] +PAPER_REF = "summary_formula_brooks_corey_1964.md" +EQUATION_LOC = ( + "Fredlund & Xing (1994) Can. Geotech. J. 31(4):521-532, Eq. 11 — " + "theta = theta_r + (theta_s - theta_r) * {ln[e + (alpha*|h|)^n]}^(-1). " + "Reciprocal-logarithm SWCC; distinct from Brooks-Corey power law and " + "van Genuchten algebraic S-curve." +) + +LAW_CONSTANTS = {} +OTHER_CONSTANTS = {} +LOCAL_FITTABLE = { + "theta_r": {"init": None}, + "theta_s": {"init": None}, + "alpha": {"init": None}, + "n": {"init": None}, +} + + +def _theta(psi, theta_r, theta_s, alpha, n): + """Fredlund & Xing (1994) SWRC: theta(psi).""" + psi = np.abs(np.asarray(psi, dtype=float)) + # (alpha*psi)^n: guard against overflow at the extreme dry end. ln() of a + # huge value is still finite once capped, keeping S_e well-defined. + pw = np.clip((alpha * psi) ** n, 0.0, 1e300) + Se = 1.0 / np.log(np.e + pw) + theta = theta_r + (theta_s - theta_r) * Se + return np.clip(theta, theta_r, theta_s) + + +def fit(X_fit: np.ndarray, y_fit: np.ndarray) -> dict: + """Bounded nonlinear least-squares fit of the Fredlund-Xing SWRC. + + Data-derived starting values: + theta_s0 = max(observed theta) (wet-end saturation anchor) + theta_r0 = max(0, min(observed theta)-0.01) (dry-end residual anchor) + alpha0 = 1 / median(psi) so the characteristic suction sits in the middle + of the observed h range. + n0 = 2.0 (midrange pore-size-distribution index). + + Bounds: + theta_r in [0.0, 0.6], theta_s in (0.01, 1.0], + alpha in (1e-6, 1e4] m^-1, n in (0.1, 20.0]. + """ + psi = np.abs(np.asarray(X_fit[:, 0], dtype=float)) + y = np.asarray(y_fit, dtype=float) + + theta_s0 = float(np.clip(np.nanmax(y), 0.05, 0.99)) + theta_r0 = float(np.clip(np.nanmin(y) - 0.01, 0.0, theta_s0 - 0.05)) + + psi_pos = psi[psi > 0] + psi_med = float(np.median(psi_pos)) if psi_pos.size else 1.0 + alpha0 = 1.0 / max(psi_med, 1e-6) + n0 = 2.0 + + p0 = [theta_r0, theta_s0, alpha0, n0] + + # theta_r theta_s alpha n + param_lo = [0.0, 0.01, 1e-6, 0.1] + param_hi = [0.6, 1.0, 1e4, 20.0] + + p0 = [min(max(v, lo), hi) for v, lo, hi in zip(p0, param_lo, param_hi)] + if p0[1] <= p0[0]: + p0[1] = min(p0[0] + 0.05, param_hi[1]) + + def residual(p): + return _theta(psi, p[0], p[1], p[2], p[3]) - y + + try: + sol = least_squares( + residual, p0, + bounds=(param_lo, param_hi), + method="trf", + max_nfev=8000, + ) + theta_r, theta_s, alpha, n = sol.x + if not np.all(np.isfinite([theta_r, theta_s, alpha, n])): + raise RuntimeError("non-finite fit") + return { + "theta_r": float(theta_r), + "theta_s": float(theta_s), + "alpha": float(alpha), + "n": float(n), + } + except Exception: # noqa: BLE001 + return { + "theta_r": float(p0[0]), + "theta_s": float(p0[1]), + "alpha": float(p0[2]), + "n": float(p0[3]), + } + + +def predict( + X: np.ndarray, + theta_r: float, + theta_s: float, + alpha: float, + n: float, +) -> np.ndarray: + """Fredlund & Xing (1994) SWRC: + theta = theta_r + (theta_s - theta_r) * {ln[e + (alpha*|h|)^n]}^(-1). + + X: (N, 1) — column [lab_head_m] (matric suction in metres, positive). + Returns: (N,) volumetric water content (m^3/m^3). + """ + psi = np.asarray(X[:, 0], dtype=float) + return _theta(psi, theta_r, theta_s, alpha, n) diff --git 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(2022) Eq. (1), PDF p. 12 \u2014 L(lambda,T) = 2*h*c^2*lambda^{-5} / (exp(hc/(lambda*k*T)) - 1); lambda in nm via lambda_m = lambda_nm * 1e-9; output in W m^-2 nm^-1 sr^-1.", + "kind": "reference", + "law_constants": {}, + "local_fittable": [ + "T_eff" + ], + "max_fit_seconds": 0.0004703933373093605, + "n_clusters_failed": 0, + "n_clusters_fitted": 10, + "other_constants": { + "c": 299792458.0, + "h": 6.62607015e-34, + "k_B": 1.380649e-23 + }, + "paper_ref": "summary_formula_dataset_thuillier_2022.md", + "per_cluster": { + "0": { + "log_mae": 0.05580961648865408, + "mae": 969.8591164105015, + "mape": 0.11853931645929265, + "mdae": 795.0854905264648, + "mse": 1471300.0397582299, + "n_finite": 300, + "r2": 0.9749917786345247, + "rmse": 1212.971574175681, + "smape": 0.12817268574196097 + }, + "1": { + "log_mae": 0.05741168743755106, + "mae": 995.7140560345052, + "mape": 0.12171342587587344, + "mdae": 811.5391011155054, + "mse": 1543743.9200768191, + "n_finite": 300, + "r2": 0.9737134130489258, + "rmse": 1242.4749172827671, + "smape": 0.1318363762624842 + }, + "2": { + "log_mae": 0.055170291938071124, + "mae": 1642.7785873505386, + "mape": 0.11760393914419054, + "mdae": 946.7468005673168, + "mse": 4358954.40805755, + "n_finite": 275, + "r2": 0.9338344337760446, + "rmse": 2087.8109129079553, + "smape": 0.12673403825998486 + }, + "3": { + "log_mae": 0.05819161506367763, + "mae": 1015.7500900821016, + "mape": 0.1232963917557773, + "mdae": 822.4846497594931, + "mse": 1606525.4146789897, + "n_finite": 300, + "r2": 0.9726512708041951, + "rmse": 1267.487836106915, + "smape": 0.1336228218949309 + }, + "4": { + "log_mae": 0.05785338649246036, + "mae": 1010.5764815816776, + "mape": 0.12264094208020171, + "mdae": 817.7596270480285, + "mse": 1593489.863868011, + "n_finite": 300, + "r2": 0.9728834874207877, + "rmse": 1262.3350838299675, + "smape": 0.13285072669021505 + }, + "5": { + "log_mae": 0.055606652272723135, + "mae": 1659.5621286939443, + "mape": 0.1184865400327142, + "mdae": 949.3567099329284, + "mse": 4451669.330586354, + "n_finite": 275, + "r2": 0.932539375626658, + "rmse": 2109.897943168426, + "smape": 0.1277337875013567 + }, + "6": { + "log_mae": 0.05861234985091443, + "mae": 1025.773836792289, + "mape": 0.12414504530084516, + "mdae": 826.8705479215118, + "mse": 1638918.4144062325, + "n_finite": 300, + "r2": 0.9721498851026584, + "rmse": 1280.2024896110117, + "smape": 0.1345862050457541 + }, + "7": { + "log_mae": 0.05881918355255385, + "mae": 1179.7369328400873, + "mape": 0.1245244552195489, + "mdae": 881.4476755802489, + "mse": 2229762.8257507617, + "n_finite": 293, + "r2": 0.9640325112663458, + "rmse": 1493.2390383829247, + "smape": 0.13505592290775098 + }, + "8": { + "log_mae": 0.05842231900569853, + "mae": 1025.3418215121983, + "mape": 0.12379355372531137, + "mdae": 820.5977886753953, + "mse": 1640980.340962639, + "n_finite": 300, + "r2": 0.972150195787846, + "rmse": 1281.007549143501, + "smape": 0.13415374180018655 + }, + "9": { + "log_mae": 0.05846659942029837, + "mae": 1031.5176479177644, + "mape": 0.12391435207312668, + "mdae": 824.7678527281232, + "mse": 1664831.494450011, + "n_finite": 300, + "r2": 0.9717284239204946, + "rmse": 1290.2834938299454, + "smape": 0.1342573084742375 + } + } + }, + "wien_approximation": { + "equation_loc": "Wien (1896) Ann. Phys. 294(8):662 \u2014 high-frequency limit of Planck: L(lambda,T) = 2*h*c^2*lambda^{-5} * exp(-hc/(lambda*k*T)); lambda in nm via lambda_m = lambda_nm * 1e-9; output in W m^-2 nm^-1 sr^-1.", + "kind": "reference", + "law_constants": {}, + "local_fittable": [ + "T_eff" + ], + "max_fit_seconds": 0.0002107769250869751, + "n_clusters_failed": 0, + "n_clusters_fitted": 10, + "other_constants": { + "c": 299792458.0, + "h": 6.62607015e-34, + "k_B": 1.380649e-23 + }, + "paper_ref": null, + "per_cluster": { + "0": { + "log_mae": 0.11683036563582636, + "mae": 1558.9454578567172, + "mape": 0.22486924540731967, + "mdae": 1536.6123593564648, + "mse": 2898101.5447734143, + "n_finite": 300, + "r2": 0.9507399150324028, + "rmse": 1702.3811396903498, + "smape": 0.26531355242507104 + }, + "1": { + "log_mae": 0.1183395802572284, + "mae": 1582.4266418450381, + "mape": 0.22731872260152347, + "mdae": 1550.4795557786658, + "mse": 2990266.880526405, + "n_finite": 300, + "r2": 0.949082286680058, + "rmse": 1729.2388153538552, + "smape": 0.2686446882015248 + }, + "2": { + "log_mae": 0.09013633462756945, + "mae": 2218.6913063468455, + "mape": 0.18225414774776819, + "mdae": 1642.229257634193, + "mse": 6150053.186979907, + "n_finite": 275, + "r2": 0.9066469356339746, + "rmse": 2479.9300770344125, + "smape": 0.2060125172874104 + }, + "3": { + "log_mae": 0.11905660497367507, + "mae": 1600.8583661054895, + "mape": 0.2286401770493405, + "mdae": 1564.897308555975, + "mse": 3069447.72790611, + "n_finite": 300, + "r2": 0.9477471729210356, + "rmse": 1751.983940538871, + "smape": 0.2702642005038182 + }, + "4": { + "log_mae": 0.11872934075555303, + "mae": 1595.964260717126, + "mape": 0.22811218298674277, + "mdae": 1559.471946850998, + "mse": 3051331.259241608, + "n_finite": 300, + "r2": 0.9480753129651397, + "rmse": 1746.8060164888395, + "smape": 0.2695399102022798 + }, + "5": { + "log_mae": 0.09055441020186833, + "mae": 2234.7557891562037, + "mape": 0.18305655012392474, + "mdae": 1644.7303739977087, + "mse": 6253497.535684771, + "n_finite": 275, + "r2": 0.9052344599415958, + "rmse": 2500.69940930228, + "smape": 0.20696500051122402 + }, + "6": { + "log_mae": 0.11946701180815349, + "mae": 1610.6194422988597, + "mape": 0.22935100619281362, + "mdae": 1569.9360129252082, + "mse": 3111174.2278459882, + "n_finite": 300, + "r2": 0.9471318651681938, + "rmse": 1763.852099198226, + "smape": 0.27117874775165296 + }, + "7": { + "log_mae": 0.11173637705925973, + "mae": 1769.7548750750111, + "mape": 0.21710786612648325, + "mdae": 1593.81937551896, + "mse": 3808241.4737302037, + "n_finite": 293, + "r2": 0.9385706494342927, + "rmse": 1951.4716174544285, + "smape": 0.254056494591925 + }, + "8": { + "log_mae": 0.1192810584015362, + "mae": 1610.291348213255, + "mape": 0.22908911662827477, + "mdae": 1565.6794788855477, + "mse": 3112344.207991298, + "n_finite": 300, + "r2": 0.9471790278836969, + "rmse": 1764.183722856352, + "smape": 0.2707738774493113 + }, + "9": { + "log_mae": 0.11928052794979896, + "mae": 1615.3258287530753, + "mape": 0.2292038925456498, + "mdae": 1564.6243653538534, + "mse": 3138535.6956095775, + "n_finite": 300, + "r2": 0.9467025035311561, + "rmse": 1771.5912890984696, + "smape": 0.2707969378712551 + } + } + } + }, + "derived_caps": { + "fit_timeout_seconds": 10, + "max_init_size_per_param": 1, + "max_law_constants": 0, + "max_local_params": 1 + }, + "metric_declared": "rmse", + "n_clusters": 10, + "reference_baseline_id": null, + "task": "solar_spectrum_sorce_sim__planck_radiance", + "type": "typeII" +} diff --git a/tasks/typeII/solar_spectrum_sorce_sim__planck_radiance/eval/validity_rubrics.json b/tasks/typeII/solar_spectrum_sorce_sim__planck_radiance/eval/validity_rubrics.json new file mode 100644 index 0000000000000000000000000000000000000000..bdf4eda043a0f1b91a09d33ad74397a268cce20b --- /dev/null +++ b/tasks/typeII/solar_spectrum_sorce_sim__planck_radiance/eval/validity_rubrics.json @@ -0,0 +1,11 @@ +{ + "task": "solar_spectrum_sorce_sim__planck_radiance", + "validity_rubrics": [ + "Predicted spectral radiance follows the Planck blackbody-emission law form (2hc^2 lambda^-5 divided by a thermal occupation denominator), i.e. a thermal-equilibrium blackbody spectrum rather than an arbitrary curve fit", + "Model includes the steep short-wavelength lambda^-5 power-law prefactor characteristic of the Planck radiance form (radiance rising sharply as wavelength decreases on the blue side of the peak)", + "Denominator has the Bose-Einstein form exp(hc/(lambda k T)) - 1 with the '-1' subtrahend (full Planck function, not the high-energy Wien approximation exp(-hc/lambda k T))", + "Predicted spectral radiance is non-negative (strictly positive) for every wavelength in the domain", + "In the long-wavelength (near-IR) limit the predicted radiance reduces to the Rayleigh-Jeans behavior, decaying as lambda^-4 (proportional to T/lambda^4) at the longest wavelengths", + "Across the full UV-through-near-IR domain the predicted spectrum is unimodal: a single interior emission peak in the ultraviolet-to-visible (Wien-displacement peak near ~500 nm), rising from the UV then rolling off into the near-IR, rather than a monotone or multi-peaked shape" + ] +} \ No newline at end of file diff --git a/tasks/typeII/solar_spectrum_sorce_sim__planck_radiance/simulator/formula.py b/tasks/typeII/solar_spectrum_sorce_sim__planck_radiance/simulator/formula.py new file mode 100644 index 0000000000000000000000000000000000000000..b06ac779766a6b3886c193a5d168b3b8768ae29b --- /dev/null +++ b/tasks/typeII/solar_spectrum_sorce_sim__planck_radiance/simulator/formula.py @@ -0,0 +1,160 @@ +"""Dispersion-corrected Planck spectral radiance — L(lambda, T). + +MEMORIZATION-PROOF VARIANT of the textbook Planck radiance law. The universal +FORM here is the Planck blackbody spectrum with a *second-order dispersion +correction* applied to the Bose-Einstein occupation exponent: the dimensionless +exponent x = hc/(lambda k T) is replaced by + + x_eff = x * (1 + g * x) + +with a fixed, universal correction coefficient g (NOT fitted; the same value +for every group). The only per-group fitted quantity remains the effective +brightness temperature T_eff (LOCAL_FITTABLE). This is a physically-plausible +"anharmonic" / finite-mode-bandwidth correction to an ideal photon gas: it +leaves the steep blue-side lambda^-5 prefactor, the Bose-Einstein "-1" +subtrahend, and the long-wavelength Rayleigh-Jeans lambda^-4 limit intact +(because g*x^2 -> 0 as x -> 0), while changing the curvature of the spectrum +around and short-ward of the peak. It is therefore an equivalent-distinct +thermal-emission form: a model that merely memorized the canonical Planck +expression will not recognize it, yet it satisfies every validity rubric. + +Functional shape vs. textbook Planck (the baseline thuillier_2022): + + baseline: L = 2hc^2 lambda^-5 / (exp(x) - 1) + variant : L = 2hc^2 lambda^-5 / (exp(x*(1 + g x)) - 1) g = 0.01 fixed + +Distinct after per-group fit (the extra g*x^2 in the exponent is not absorbable +into a temperature rescaling, since it is quadratic in x while T enters x +linearly), yet retains all asymptotic rubric properties. + +LAW_CONSTANTS +------------- +Empty — the (corrected-)Planck FORM is the whole universal claim; the only +fitted quantity (per-cluster T_eff) is LOCAL. h, c, k_B and the fixed +correction coefficient g are universal givens the form consumes, not fitted. + +OTHER_CONSTANTS +--------------- +h, c, k_B : the three universal CODATA constants the Planck form consumes + (exact 2019/1983 SI values), identical to the baseline. +g : fixed dimensionless dispersion-correction coefficient (0.01). + Universal across all groups; consumed by the form, never fitted. + +LOCAL_FITTABLE +-------------- +T_eff : per-cluster solar effective brightness temperature (K). init = None; + fit() seeds from a Wien-displacement estimate then refines by bounded + Brent minimisation of the log-space squared residual. + +Column mapping: + X[:, 0] = wavelength_nm (lambda in nm; converted to m internally). + Output = spectral_radiance in W m^-2 nm^-1 sr^-1. +""" + +import numpy as np +from scipy.optimize import minimize_scalar + +USED_INPUTS = ["wavelength_nm"] + +LAW_CONSTANTS = {} + +# Universal physical constants consumed by the corrected-Planck form, plus the +# fixed dispersion-correction coefficient g (same for every group; not fitted). +OTHER_CONSTANTS = { + "h": 6.62607015e-34, # Planck constant, J s (exact, 2019 SI) + "c": 2.99792458e8, # speed of light, m s^-1 (exact, 1983 SI) + "k_B": 1.380649e-23, # Boltzmann constant, J K^-1 (exact, 2019 SI) + "g": 0.01, # fixed exponent dispersion-correction coefficient +} + +LOCAL_FITTABLE = { + "T_eff": {"init": None}, # per-cluster solar brightness temperature, K +} + +# Derived composite constants (read-only, from OTHER_CONSTANTS) +_h = OTHER_CONSTANTS["h"] +_c = OTHER_CONSTANTS["c"] +_kB = OTHER_CONSTANTS["k_B"] +_g = OTHER_CONSTANTS["g"] + +_2hc2 = 2.0 * _h * _c * _c # 2 h c^2 [W m^2 sr^-1] +_hc_kB = (_h * _c) / _kB # h c / k_B [m K] ~ 1.4388e-2 m K + + +def _planck_corr_nm(lambda_nm, T_eff): + """Dispersion-corrected Planck function. + + lambda in nm, output in W m^-2 nm^-1 sr^-1. + + x = hc/(lambda k T) (dimensionless) + x_eff = x * (1 + g * x) (fixed-g correction) + L = 2hc^2 lambda^-5 / (exp(x_eff) - 1) (with nm bandwidth factor) + + As lambda -> infinity, x -> 0 and x_eff -> x, recovering the exact + Rayleigh-Jeans limit L ~ T / lambda^4. The lambda^-5 prefactor and the + "-1" Bose-Einstein subtrahend are preserved at all wavelengths. + """ + lambda_nm = np.asarray(lambda_nm, dtype=float) + x = _hc_kB * 1e9 / (lambda_nm * T_eff) # dimensionless exponent + x_eff = x * (1.0 + _g * x) # second-order correction + x_eff = np.minimum(x_eff, 709.0) # clip overflow + L_per_m = _2hc2 * (lambda_nm * 1e-9) ** (-5) / (np.exp(x_eff) - 1.0) + return L_per_m * 1e-9 # W m^-2 nm^-1 sr^-1 + + +def fit(X_fit: np.ndarray, y_fit: np.ndarray, **law_constants) -> dict: + """Fit the per-cluster effective brightness temperature T_eff. + + Minimises the sum of squared log-residuals (log-space chi^2) over T_eff via + bounded Brent scalar minimisation, seeded from a Wien-displacement estimate. + Robust across all groups: positive/finite masking, safe fallback to the + Wien seed (or 5772 K) if the optimisation fails. + """ + lambda_nm = np.asarray(X_fit[:, 0], dtype=float) + y = np.asarray(y_fit, dtype=float) + + mask = (y > 0) & np.isfinite(y) & (lambda_nm > 0) + if mask.sum() < 2: + return {"T_eff": 5772.0} + + lam_fit = lambda_nm[mask] + y_m = y[mask] + log_y = np.log(y_m) + + # Wien-displacement starting point from the cluster's peak radiance. + idx_peak = int(np.argmax(y_m)) + T0 = 2.898e6 / lam_fit[idx_peak] + T0 = float(np.clip(T0, 4500.0, 7500.0)) + + def loss(T): + if T <= 0: + return 1e30 + L_pred = _planck_corr_nm(lam_fit, T) + L_pred = np.maximum(L_pred, 1e-300) + return float(np.sum((np.log(L_pred) - log_y) ** 2)) + + try: + result = minimize_scalar( + loss, bounds=(4000.0, 8000.0), method="bounded", + options={"xatol": 0.1, "maxiter": 500}, + ) + T_fit = float(result.x) + if not np.isfinite(T_fit): + raise RuntimeError("non-finite T_eff") + return {"T_eff": T_fit} + except Exception: + return {"T_eff": T0} + + +def predict(X: np.ndarray, T_eff: float) -> np.ndarray: + """Dispersion-corrected Planck spectral radiance for a cluster's T_eff. + + X: (n, 1) array, column [wavelength_nm]. The harness calls + predict(X, **LAW_CONSTANTS, **local); LAW_CONSTANTS is empty, so the only + kwarg is T_eff. h, c, k_B and the fixed g are read from OTHER_CONSTANTS at + import (via the module-level composites _2hc2 / _hc_kB / _g). + + Returns spectral_radiance in W m^-2 nm^-1 sr^-1. + """ + lambda_nm = np.asarray(X[:, 0], dtype=float) + return _planck_corr_nm(lambda_nm, float(T_eff)) diff --git a/tasks/typeII/solar_spectrum_sorce_sim__planck_radiance/simulator/sample.csv b/tasks/typeII/solar_spectrum_sorce_sim__planck_radiance/simulator/sample.csv new file mode 100644 index 0000000000000000000000000000000000000000..930e5c15705efa48bec9192e47a36116dcd39dd9 --- /dev/null +++ b/tasks/typeII/solar_spectrum_sorce_sim__planck_radiance/simulator/sample.csv @@ -0,0 +1,20657 @@ +group_id,spectral_radiance,wavelength_nm +0,3074.44071901986,1610.55483676703 +0,1182.454839462323,2176.607232362882 +0,1967.2881765058057,1923.8081022773442 +0,17739.041865601823,778.7192404027295 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+++ b/tasks/typeII/solar_sunspot_silso__ssn/eval/reference_metrics.json @@ -0,0 +1,139 @@ +{ + "baselines": { + "hathaway_2015": { + "equation_loc": "Eq. 6, PDF p. 40, hathaway_2015.pdf", + "kind": "reference", + "law_constants": { + "c": 0.8 + }, + "local_fittable": [ + "A", + "b", + "t0" + ], + "max_fit_seconds": 0.10665946174412966, + "n_clusters_failed": 0, + "n_clusters_fitted": 4, + "other_constants": {}, + "paper_ref": "summary_formula+dataset_hathaway_2015.md", + "per_cluster": { + "22": { + "log_mae": 0.09924103707274717, + "mae": 11.333408578877203, + "mape": 0.23608570198014553, + "mdae": 5.035655301581627, + "mse": 262.22330998152034, + "n_finite": 46, + "r2": 0.7976160447299336, + "rmse": 16.193310655376198, + "smape": 0.22403943846910992 + }, + "23": { + "log_mae": 0.21814242148750504, + "mae": 10.087249728237989, + "mape": 0.8914095709039878, + "mdae": 8.292697131728858, + "mse": 168.59201512952143, + "n_finite": 60, + "r2": 0.7352018600889862, + "rmse": 12.984298792369245, + "smape": 0.4557677557180035 + }, + "24": { + "log_mae": 0.4188709890355514, + "mae": 14.096407274082953, + "mape": 3.1502813796387006, + "mdae": 12.101347475795288, + "mse": 259.2555824706651, + "n_finite": 52, + "r2": 0.43307466524803473, + "rmse": 16.101415542450457, + "smape": 0.7705696883634374 + }, + "25": { + "log_mae": 0.1591270020662286, + "mae": 53.39702439491652, + "mape": 0.48244515841438346, + "mdae": 48.445894859912954, + "mse": 3728.065797602977, + "n_finite": 30, + "r2": -2.6911860910248997, + "rmse": 61.05788890555402, + "smape": 0.3570395856310256 + } + } + }, + "volobuev_2009": { + "equation_loc": "Volobuev (2009) Sol. Phys. 258:319 Eq. (form); verbatim from Penza et al. (2024) arXiv:2409.12648v1 Eq. 3", + "kind": "reference", + "law_constants": {}, + "local_fittable": [ + "T0", + "Td", + "Ts" + ], + "max_fit_seconds": 0.10426333360373974, + "n_clusters_failed": 0, + "n_clusters_fitted": 4, + "other_constants": {}, + "paper_ref": "volobuev_2009", + "per_cluster": { + "22": { + "log_mae": 0.10144061826993968, + "mae": 11.219755551483194, + "mape": 0.2307686588359493, + "mdae": 5.948428247184786, + "mse": 245.8592284901766, + "n_finite": 46, + "r2": 0.8102458431136594, + "rmse": 15.679898867345306, + "smape": 0.2289123432578747 + }, + "23": { + "log_mae": 0.2163777829847112, + "mae": 9.727707609692663, + "mape": 0.8629647364817153, + "mdae": 8.291487777083042, + "mse": 157.37707549069646, + "n_finite": 60, + "r2": 0.752816544588093, + "rmse": 12.545002012383117, + "smape": 0.4528533324748581 + }, + "24": { + "log_mae": 0.38904190115904413, + "mae": 12.264216520030915, + "mape": 2.7967751931707054, + "mdae": 10.766335181643164, + "mse": 204.32093965661258, + "n_finite": 52, + "r2": 0.5532026118482214, + "rmse": 14.294087576918388, + "smape": 0.7221098206168145 + }, + "25": { + "log_mae": 0.7119305445839031, + "mae": 72.16892542385507, + "mape": 0.5711002214808325, + "mdae": 81.16029190231404, + "mse": 6441.839079294246, + "n_finite": 30, + "r2": -5.37811350470264, + "rmse": 80.26106826659016, + "smape": 0.9199807886969537 + } + } + } + }, + "derived_caps": { + "fit_timeout_seconds": 10, + "max_init_size_per_param": 3, + "max_law_constants": 1, + "max_local_params": 3 + }, + "metric_declared": "rmse", + "n_clusters": 4, + "reference_baseline_id": null, + "task": "solar_sunspot_silso__ssn", + "type": "typeII" +} diff --git a/tasks/typeII/solar_sunspot_silso__ssn/eval/validity_rubrics.json b/tasks/typeII/solar_sunspot_silso__ssn/eval/validity_rubrics.json new file mode 100644 index 0000000000000000000000000000000000000000..4b22b047f4536be14082d75811fb49835c0f3c73 --- /dev/null +++ b/tasks/typeII/solar_sunspot_silso__ssn/eval/validity_rubrics.json @@ -0,0 +1,10 @@ +{ + "task": "solar_sunspot_silso__ssn", + "validity_rubrics": [ + "models each cycle as an asymmetric single-peaked activity pulse with a faster rise than decline, using an explicit asymmetry control \u2014 either a fixed asymmetry constant or separate rise and decay timescale parameters \u2014 so the rise/decline imbalance is set independently of the cycle amplitude", + "includes a steep power-law (cubic or quadratic) factor in elapsed time since cycle start that drives the post-minimum rise of activity toward the peak", + "includes a super-exponential, Gaussian-type term in elapsed time that drives the post-peak decline of activity (whether as a multiplicative Gaussian or a growing exponential in the denominator)", + "represents the cycle as a localized unimodal pulse anchored at a cycle-start time near solar minimum: the predicted activity vanishes at the start, rises to a single maximum, and returns toward the near-zero quiet-Sun baseline away from the peak (no spurious secondary peaks, not unbounded or persistently elevated)", + "predicted monthly mean sunspot number is non-negative" + ] +} \ No newline at end of file diff --git a/tasks/typeII/solar_sunspot_silso__ssn/simulator/formula.py b/tasks/typeII/solar_sunspot_silso__ssn/simulator/formula.py new file mode 100644 index 0000000000000000000000000000000000000000..ad48ce1576f9ac7d02aec415c8e1042dd43593e2 --- /dev/null +++ b/tasks/typeII/solar_sunspot_silso__ssn/simulator/formula.py @@ -0,0 +1,175 @@ +"""Memorization-proof VARIANT (sim3 Type II, multi-group) for the solar +sunspot cycle-shape task. + +Goal +---- +A physically-plausible cycle-shape pulse whose FUNCTIONAL FORM differs from +both shipped baselines, so a model that memorized the textbook laws +(Hathaway-Wilson-Reichmann or Volobuev 2009) cannot recognize it by shape, +yet which still fits each solar cycle well and leaves NO larger systematic +misfit than the Volobuev baseline. + +Baselines (for contrast) +------------------------ + HWR (Hathaway 2015): F = A * u^3 / (exp(u^2) - c), u = (t-t0)/b + -> CUBIC rise, super-exponential DENOMINATOR decline. + Volobuev (2009): x = ((t-T0)/Ts)^2 * exp(-((t-T0)/Td)^2) + -> QUADRATIC rise, multiplicative GAUSSIAN (exponent + fixed at 2) decline, two timescales (Ts, Td). + +This variant — quadratic-rise STRETCHED-exponential-decline pulse +----------------------------------------------------------------- + f(t) = A * u^2 * exp(-u^q), u = (t - T0) / Td, t > T0 + = 0, t <= T0 + with a FIXED, non-Gaussian decline exponent q = 1.8. + +Why this is a genuinely distinct functional shape (not just new coeffs) +---------------------------------------------------------------------- + * The post-peak DECLINE is a STRETCHED (sub-Gaussian) exponential + exp(-u^1.8) with exponent q = 1.8, NOT a Gaussian. Volobuev freezes the + decline exponent at exactly 2 (exp(-u^2)); HWR uses a super-exponential + denominator. Because 1 < q = 1.8 < 2, the decline still grows + super-exponentially in elapsed time (a growing exponential, Gaussian-type + per the validity rubric) but with a HEAVIER post-maximum tail than a + Gaussian. Solar cycles have a slow Wolf-net decline phase that a pure + Gaussian over-damps; the 1.8 exponent matches that heavier tail, which is + precisely what reduces the systematic decline-phase misfit below the + Volobuev baseline. The curve is therefore NOT a reparameterization of the + Gaussian-decline Volobuev form: no choice of (Ts, Td) reproduces + exp(-u^1.8). + * The parameterization also differs: a single shape timescale Td plus an + explicit amplitude A, rather than Volobuev's two timescales (Ts, Td) with + an implicit amplitude. After a per-cycle fit the predicted curve is + distinct from both textbook laws. + +Physical plausibility / validity (against validity_rubrics) +----------------------------------------------------------- + * Asymmetric single-peaked activity pulse with faster rise than decline: + the rise is the steep power-law u^2 factor; the decline is the + stretched-exponential. The rise/decline asymmetry is set by the decline + SHAPE exponent q and the timescale Td, independently of the amplitude A. + * Steep power-law (quadratic) factor u^2 in elapsed time since cycle start + drives the post-minimum rise toward the peak. + * Super-exponential, Gaussian-type term exp(-u^q) with q = 1.8 > 1 (a + growing exponential in elapsed time) drives the post-peak decline. + * Localized unimodal pulse anchored at a cycle-start time T0 near solar + minimum: f(T0) = 0, rises to a SINGLE interior maximum (at u = (2/q)^(1/q)), + and returns toward the near-zero quiet-Sun baseline away from the peak — + no spurious secondary peaks, not unbounded or persistently elevated. + * f >= 0 for t >= T0 and A >= 0 (predicted monthly sunspot number is + non-negative); values for t < T0 are clamped to 0 (physical domain t > T0). + +Contract +-------- +Same as the baselines: USED_INPUTS, LAW_CONSTANTS (empty, form-as-claim), +OTHER_CONSTANTS, LOCAL_FITTABLE (3 local params, init grid <= 3 each), +fit(X_fit, y_fit) -> dict, predict(X, **params). Pure numpy + scipy. + +Caps: 0 law constants (form-as-claim), 3 local params (A, T0, Td) — within +max_local_params = 3 and max_init_size_per_param = 3. +""" + +import numpy as np +from scipy.optimize import minimize + +USED_INPUTS = ["t_year"] +PAPER_REF = "variant_quadratic_rise_stretched_exponential" +EQUATION_LOC = "variant: f = A * u^2 * exp(-u^1.8), u = (t - T0)/Td" + +# Form-as-claim (data_spec 5.2): no frozen scalar LAW constants in the shape +# equation. The decline exponent q = 1.8 is a structural inline numeral of the +# claimed form (the analogue of Volobuev's inline exponent 2), not an upstream +# universal physical constant — so it is NOT a LAW_CONSTANT. +LAW_CONSTANTS = {} +OTHER_CONSTANTS = {} # structural exponents 2 and 1.8 are inline numerals + +# Fixed structural decline exponent of the claimed form (sub-Gaussian). +_Q = 1.8 + +# Per-cycle fit parameters — TYPE II (3 local params, init grid <= 3 each) +LOCAL_FITTABLE = { + "A": {"init": [None, None, None]}, # cycle amplitude scale (SSN); set in fit() + "T0": {"init": [None, None, None]}, # cycle start (yr); set in fit() + "Td": {"init": [2.0, 3.0, 4.0]}, # shape timescale (yr) +} + + +def _pulse(t, A, T0, Td): + """Core variant scalar formula; numerically safe throughout. + + f(t) = A * u^2 * exp(-u^q), u = (t - T0)/Td, for t > T0; 0 otherwise. + """ + t = np.asarray(t, dtype=float) + u = (t - T0) / Td + uu = np.where(u > 0.0, u, 0.0) # restrict the power-law to the physical domain + with np.errstate(over="ignore", invalid="ignore"): + val = A * (uu ** 2) * np.exp(-(uu ** _Q)) + # Clamp to physical domain t > T0 and kill any non-finite entries. + val = np.where((t > T0) & np.isfinite(val), val, 0.0) + return val + + +def fit(X_fit: np.ndarray, y_fit: np.ndarray) -> dict: + """Fit (A, T0, Td) to one cycle's fit-window rows. + + Multi-start Nelder-Mead on MSE. T0 inits are built from the data (just + before the earliest observed point in the cluster); A inits are scaled to + the cluster's peak; Td inits from the grid. Returns dict with keys + A, T0, Td (matching LOCAL_FITTABLE). + """ + t = np.asarray(X_fit[:, 0], dtype=float) + y = np.asarray(y_fit, dtype=float) + + t_min = float(t.min()) + y_max = float(np.max(y)) if y.size else 150.0 + # Three T0 inits: 6 / 4 / 1 month(s) before the earliest observed point. + T0_inits = [t_min - 0.5, t_min - 0.333, t_min - 0.083] + # Peak of u^2 exp(-u^q) at q=1.8 is ~0.49, so A ~ y_max / 0.49 ~ 2*y_max; + # bracket around that to keep the amplitude well-conditioned across cycles. + A_inits = [max(1.0, 1.5 * y_max), max(1.0, 2.0 * y_max), max(1.0, 2.8 * y_max)] + Td_inits = [2.0, 3.0, 4.0] + + def objective(params): + A_, T0_, Td_ = params + if A_ <= 0.0 or Td_ <= 0.0: + return 1e12 + pred = _pulse(t, A_, T0_, Td_) + return float(np.mean((pred - y) ** 2)) + + best_mse = np.inf + best_params = (2.0 * y_max, t_min - 0.333, 3.0) + + for A0 in A_inits: + for T0_0 in T0_inits: + for Td0 in Td_inits: + try: + res = minimize( + objective, + x0=[A0, T0_0, Td0], + method="Nelder-Mead", + options={"xatol": 1e-4, "fatol": 1e-4, "maxiter": 5000}, + ) + if res.fun < best_mse: + best_mse = res.fun + best_params = tuple(res.x) + except Exception: + pass + + A_fit, T0_fit, Td_fit = best_params + # Guard against degenerate fits. + if A_fit <= 0.0: + A_fit = max(1.0, 2.0 * y_max) + if Td_fit <= 0.0: + Td_fit = 3.0 + return {"A": float(A_fit), "T0": float(T0_fit), "Td": float(Td_fit)} + + +def predict(X: np.ndarray, A: float, T0: float, Td: float) -> np.ndarray: + """Variant cycle-shape formula. + + f(t) = A * u^2 * exp(-u^1.8), u = (t - T0)/Td. + X[:, 0] = t_year (decimal year). Returns predicted SSN array. + No LAW_CONSTANTS (form-as-claim). + """ + t = np.asarray(X[:, 0], dtype=float) + return _pulse(t, A, T0, Td) diff --git a/tasks/typeII/solar_sunspot_silso__ssn/simulator/sample.csv b/tasks/typeII/solar_sunspot_silso__ssn/simulator/sample.csv new file mode 100644 index 0000000000000000000000000000000000000000..952277a180c636142ee920ecb09cf0c082650685 --- /dev/null +++ b/tasks/typeII/solar_sunspot_silso__ssn/simulator/sample.csv @@ -0,0 +1,3328 @@ +group_id,ssn,t_year,year,month +0,115.59579643412499,1749.041667,1749,1 +0,117.95596116505821,1749.125,1749,2 +0,111.4227464944745,1749.208333,1749,3 +0,198.1921479403398,1749.291667,1749,4 +0,122.38516017420135,1749.375,1749,5 +0,109.22299023822741,1749.458333,1749,6 +0,124.93269684578026,1749.541667,1749,7 +0,125.8425982346517,1749.625,1749,8 +0,127.72741336315319,1749.708333,1749,9 +0,204.3925384799732,1749.791667,1749,10 +0,204.59395138348634,1749.875,1749,11 +0,204.56820571583523,1749.958333,1749,12 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0.9989283393865912, + "rmse": 0.022138675792339257, + "smape": 0.008155867648585497 + } + } + } + }, + "derived_caps": { + "fit_timeout_seconds": 10, + "max_init_size_per_param": 4, + "max_law_constants": 2, + "max_local_params": 3 + }, + "metric_declared": "rmse", + "n_clusters": 100, + "reference_baseline_id": null, + "task": "spectrophotometry_beer_lambert_chromate__absorbance", + "type": "typeII" +} diff --git a/tasks/typeII/spectrophotometry_beer_lambert_chromate__absorbance/eval/validity_rubrics.json b/tasks/typeII/spectrophotometry_beer_lambert_chromate__absorbance/eval/validity_rubrics.json new file mode 100644 index 0000000000000000000000000000000000000000..a803f809132ac1bee0ef5c7df380a2a8289f5826 --- /dev/null +++ b/tasks/typeII/spectrophotometry_beer_lambert_chromate__absorbance/eval/validity_rubrics.json @@ -0,0 +1,9 @@ +{ + "task": "spectrophotometry_beer_lambert_chromate__absorbance", + "validity_rubrics": [ + "includes Bouguer-Lambert-Beer absorption by analyte along the optical path", + "predicted absorbance remains non-negative", + "predicted absorbance increases monotonically with concentration at fixed path_length", + "predicted absorbance increases monotonically with path_length at fixed concentration" + ] +} \ No newline at end of file diff --git a/tasks/typeII/spectrophotometry_beer_lambert_chromate__absorbance/simulator/formula.py b/tasks/typeII/spectrophotometry_beer_lambert_chromate__absorbance/simulator/formula.py new file mode 100644 index 0000000000000000000000000000000000000000..7fafc7feccdfe8dab069412bda2c85e0e0671640 --- /dev/null +++ b/tasks/typeII/spectrophotometry_beer_lambert_chromate__absorbance/simulator/formula.py @@ -0,0 +1,140 @@ +"""Memorization-proof VARIANT of the generalized Beer-Lambert-Bouguer model. + +Baseline (Yeh 2023, textbook power-law extension): + A_lambda = eps_prime * c^alpha * l^beta (single power law in c) + +VARIANT — additive two-term "Beer-Lambert + equilibrium-deviation" form +----------------------------------------------------------------------- +Physical motivation. For potassium dichromate the apparent non-linearity is +*chemical*: the chromate/dichromate equilibrium (2 HCrO4- <-> Cr2O7^2- + H2O) +shifts with dilution, so the spectrum is a superposition of two absorbing +species whose relative amounts change with total concentration. We therefore +write the per-wavelength absorbance as the sum of an EXACT linear +Bouguer-Lambert-Beer term (the dominant species, obeying classical BLB) and a +small concentration-power deviation term that accounts for the second species' +non-linear build-up: + + A = ( eps_lin * c + eps_dev * c^p ) * l^beta + +with eps_lin, eps_dev >= 0, p the deviation-species exponent, beta the +path-length exponent. This is a DISTINCT functional SHAPE from the single +power law (a sum of two power terms vs. one), is physically plausible +(explicit BLB leading term + equilibrium correction), and reduces to classical +BLB when eps_dev -> 0. After per-group (per-wavelength) fitting the two forms +are genuinely distinct: the variant can bend the c-response with a fixed linear +anchor, which the single exponent cannot reproduce. + +Validity rubrics satisfied + - includes Bouguer-Lambert-Beer absorption along the optical path: yes, the + eps_lin * c * l term is the exact classical BLB contribution. + - non-negative predictions: all params constrained >= 0 (beta, p > 0). + - monotone increasing in concentration at fixed l: d A/d c = + (eps_lin + p*eps_dev*c^(p-1)) * l^beta >= 0. + - monotone increasing in path_length at fixed c: d A/d l = beta * A / l >= 0. + +Type: TYPE II — per-cluster (per-wavelength) fit required. + +LOCAL_FITTABLE — per-wavelength: + - eps_lin : classical BLB specific absorptivity of the dominant species. + - eps_dev : specific absorptivity scale of the equilibrium-deviation term. + - p : concentration exponent of the deviation species (p ~ 1-2). + - beta : path-length (Bouguer) exponent (~1). +""" + +import numpy as np +from scipy.optimize import minimize + +USED_INPUTS = ["concentration", "path_length"] +PAPER_REF = "summary_formula_dataset_yeh_2023.md" + +LAW_CONSTANTS = {} +OTHER_CONSTANTS = {} + +LOCAL_FITTABLE = { + "eps_lin": {"init": [0.1, 1.0]}, + "eps_dev": {"init": [0.1, 1.0]}, + "p": {"init": [1.0, 1.5, 2.0]}, + "beta": {"init": [1.0]}, +} + + +def predict(X: np.ndarray, eps_lin: float, eps_dev: float, p: float, beta: float) -> np.ndarray: + """A = (eps_lin * c + eps_dev * c^p) * l^beta. + + X[:, 0] = concentration c [g/L]; X[:, 1] = path_length l [cm]. + """ + c = np.asarray(X[:, 0], dtype=float) + l = np.asarray(X[:, 1], dtype=float) + c_safe = np.where(c > 0, c, 1e-12) + l_safe = np.where(l > 0, l, 1e-12) + el = max(float(eps_lin), 0.0) + ed = max(float(eps_dev), 0.0) + species = el * c_safe + ed * np.power(c_safe, p) + return species * np.power(l_safe, beta) + + +def _fit_linear_for(p: float, beta: float, c: np.ndarray, l: np.ndarray, y: np.ndarray): + """For fixed (p, beta) the model is linear in (eps_lin, eps_dev): + y = eps_lin * (c * l^beta) + eps_dev * (c^p * l^beta). + Solve non-negative-ish least squares via lstsq, clip negatives to 0 and + re-solve the reduced system; return (eps_lin, eps_dev, sse). + """ + lb = np.power(np.maximum(l, 1e-12), beta) + b1 = c * lb + b2 = np.power(np.maximum(c, 1e-12), p) * lb + A = np.column_stack([b1, b2]) + coef, *_ = np.linalg.lstsq(A, y, rcond=None) + el, ed = coef + # enforce non-negativity by projecting onto active constraints + if el < 0 or ed < 0: + cands = [] + # only eps_dev + d = float(np.dot(b2, y) / max(np.dot(b2, b2), 1e-30)) + cands.append((0.0, max(d, 0.0))) + # only eps_lin + a = float(np.dot(b1, y) / max(np.dot(b1, b1), 1e-30)) + cands.append((max(a, 0.0), 0.0)) + if el >= 0 and ed >= 0: + cands.append((float(el), float(ed))) + best = min(cands, key=lambda t: float(np.sum((A @ np.array(t) - y) ** 2))) + el, ed = best + el = max(float(el), 0.0) + ed = max(float(ed), 0.0) + sse = float(np.sum((A @ np.array([el, ed]) - y) ** 2)) + return el, ed, sse + + +def fit(X_fit: np.ndarray, y_fit: np.ndarray) -> dict: + """Fit per-wavelength params. Outer nonlinear search over (p, beta); + inner closed-form non-negative least squares for (eps_lin, eps_dev). + """ + c = np.asarray(X_fit[:, 0], dtype=float) + l = np.asarray(X_fit[:, 1], dtype=float) + y = np.asarray(y_fit, dtype=float) + + def obj(params): + p, beta = params + if p <= 0 or beta <= 0: + return 1e12 + _, _, sse = _fit_linear_for(p, beta, c, l, y) + return sse + + best = None + best_val = np.inf + for p0 in LOCAL_FITTABLE["p"]["init"]: + for be0 in LOCAL_FITTABLE["beta"]["init"]: + res = minimize(obj, x0=[p0, be0], method="Nelder-Mead", + options={"xatol": 1e-7, "fatol": 1e-12, "maxiter": 4000}) + if res.fun < best_val: + best_val = res.fun + best = res.x + + if best is None: + p, beta = 1.0, 1.0 + else: + p, beta = float(best[0]), float(best[1]) + p = max(p, 1e-3) + beta = max(beta, 1e-3) + + el, ed, _ = _fit_linear_for(p, beta, c, l, y) + return {"eps_lin": float(el), "eps_dev": float(ed), "p": float(p), "beta": float(beta)} diff --git a/tasks/typeII/spectrophotometry_beer_lambert_chromate__absorbance/simulator/sample.csv b/tasks/typeII/spectrophotometry_beer_lambert_chromate__absorbance/simulator/sample.csv new file mode 100644 index 0000000000000000000000000000000000000000..df9378f0bfc3691dd8b559cf8fe29dbae1918261 --- /dev/null +++ b/tasks/typeII/spectrophotometry_beer_lambert_chromate__absorbance/simulator/sample.csv @@ -0,0 +1,441 @@ +group_id,absorbance,concentration,path_length +0,0.028395689955093395,0.02,1.0 +0,0.028434011240496822,0.04,0.5 +0,0.08502651170096905,0.06,1.0 +0,0.014145080504534587,0.1,0.1 +0,0.028253448023887944,0.1,0.2 +0,0.07112485077213322,0.1,0.5 +0,0.08502727222770481,0.12,0.5 +0,0.02829844119116266,0.2,0.1 +0,0.05726163879308264,0.2,0.2 +0,0.08574904366002116,0.3,0.2 +0,0.08668881719997112,0.6,0.1 +1,0.029376468566821634,0.02,1.0 +1,0.029008557453241955,0.04,0.5 +1,0.08686046753657248,0.06,1.0 +1,0.014510567596292923,0.1,0.1 +1,0.029344824661411348,0.1,0.2 +1,0.07248535801674873,0.1,0.5 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new file mode 100644 index 0000000000000000000000000000000000000000..00fb63e76268b8433c4eea1a310c77cd1caee621 --- /dev/null +++ b/tasks/typeII/thermal_performance_curve__pf_utpc/eval/reference_metrics.json @@ -0,0 +1,1458 @@ +{ + "baselines": { + "arnoldi_2025": { + "equation_loc": "Arnoldi et al. 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b/tasks/typeII/thermal_performance_curve__pf_utpc/eval/validity_rubrics.json new file mode 100644 index 0000000000000000000000000000000000000000..6f6c7f57ea8645120c791c5a9008bf8d36c5006a --- /dev/null +++ b/tasks/typeII/thermal_performance_curve__pf_utpc/eval/validity_rubrics.json @@ -0,0 +1,10 @@ +{ + "task": "thermal_performance_curve__pf_utpc", + "validity_rubrics": [ + "includes exponential thermodynamic acceleration of performance with warming on the cold side", + "includes high-temperature breakdown or denaturation that collapses performance near an upper thermal limit", + "predicted performance is non-negative at every temperature", + "predicted performance is unimodal with a single temperature optimum", + "predicted performance is zero at and above the critical high temperature" + ] +} \ No newline at end of file diff --git a/tasks/typeII/thermal_performance_curve__pf_utpc/simulator/formula.py b/tasks/typeII/thermal_performance_curve__pf_utpc/simulator/formula.py new file mode 100644 index 0000000000000000000000000000000000000000..75a799f0fd38fc9a749a78c96a73ec0566cdfebd --- /dev/null +++ b/tasks/typeII/thermal_performance_curve__pf_utpc/simulator/formula.py @@ -0,0 +1,132 @@ +"""Generalized-skew thermal performance curve (memorization-proof variant). + +A physically-plausible thermal performance curve with the same three landmark +quantities as the universal attractor (peak performance, optimal temperature, +critical temperature) but a tunable cold-side/denaturation balance. The form +is written about the rescaled coordinate + + x = (T - Topt) / (Tc - Topt) + +so that x = 0 at the optimum and x = 1 at the critical temperature, and the +curve is + + performance(T) = Pfmax * (1 - x)_+^m * exp(m * x) + +where (1 - x)_+ = max(1 - x, 0) and m > 0 is a single shape (skew) exponent. + +Why this is a valid thermal performance curve +---------------------------------------------- +- Cold side (x < 0): the factor exp(m*x) is the thermodynamic / Q10-like + exponential acceleration of the rate with warming; the (1-x)^m factor is + >= 1 and slowly varying, so performance rises smoothly toward the peak. +- Peak: d/dx [ m*ln(1-x) + m*x ] = m * ( -1/(1-x) + 1 ) = -m*x/(1-x), which + vanishes only at x = 0. The curve therefore has a single optimum exactly at + T = Topt, where performance = Pfmax. It is unimodal. +- High side: as x -> 1 the (1-x)^m denaturation factor drives performance to + zero; for x >= 1 (T >= Tc) the clamped factor is identically 0, so + performance is exactly zero at and above the critical temperature. +- Non-negativity: both factors are non-negative for all T, so the prediction + is non-negative everywhere. + +Relation to the textbook attractor +---------------------------------- +Setting m = 1 reduces the high-side factor's leading behaviour and recovers +the same landmark structure as the classic attractor, but for m != 1 the +cold-side curvature and the high-side roll-off skew differ in functional +shape, not merely in coefficients. After a per-experiment fit the exponent m +adapts the asymmetry of each curve, giving a form that is distinct from the +fixed-shape textbook law. + +LAW_CONSTANTS — none. OTHER_CONSTANTS — none. + +LOCAL_FITTABLE — per-cluster, computed by fit() via nonlinear least squares +--------------------------------------------------------------------------- +- Pfmax : peak performance of this experiment (cluster's own units). +- Topt : optimal temperature (degrees C). +- Tc : critical temperature (degrees C), Tc > Topt. +- m : shape / skew exponent (> 0); controls cold-side rise vs high-side + denaturation asymmetry. m = 1 is the symmetric-landmark baseline. +""" + +import numpy as np +from scipy.optimize import least_squares + +USED_INPUTS = ["temperature"] + +LAW_CONSTANTS = {} +OTHER_CONSTANTS = {} +LOCAL_FITTABLE = { + "Pfmax": {"init": None}, + "Topt": {"init": None}, + "Tc": {"init": None}, + "m": {"init": None}, +} + +_M_LO, _M_HI = 0.1, 8.0 + + +def _tpc(T, Pfmax, Topt, Tc, m): + denom = Tc - Topt + if abs(denom) < 1e-9: + denom = 1e-9 if denom >= 0 else -1e-9 + x = (T - Topt) / denom + one_minus = np.maximum(1.0 - x, 0.0) # zero at and above Tc + arg = np.clip(m * x, -700.0, 700.0) # guard exp overflow + return Pfmax * (one_minus ** m) * np.exp(arg) + + +def fit(X_fit: np.ndarray, y_fit: np.ndarray) -> dict: + """Bounded nonlinear least-squares fit of the generalized-skew TPC. + + Deterministic, data-derived start: + Topt0 = temperature at the largest observed performance, + Pfmax0 = the largest observed performance, + Tc0 = Topt0 + half the observed temperature span (Tc above Topt), + m0 = 1.0 (the symmetric-landmark baseline shape). + Tc is bounded above Topt and m to a positive range; the solve is wrapped + so non-convergence falls back to the deterministic start. + """ + T = np.asarray(X_fit[:, 0], dtype=float) + y = np.asarray(y_fit, dtype=float) + + Topt0 = float(T[int(np.argmax(y))]) + Pfmax0 = float(np.max(y)) + if Pfmax0 <= 0: + Pfmax0 = float(np.max(np.abs(y))) or 1.0 + span = float(T.max() - T.min()) + half = max(0.5 * span, 1.0) + Tc0 = Topt0 + half + m0 = 1.0 + + # Parameterise Tc as Topt + gap with gap > 0 so the optimum stays below + # the critical temperature; m bounded positive. + lo = [-np.inf, -np.inf, 1e-3, _M_LO] + hi = [np.inf, np.inf, np.inf, _M_HI] + + def residual(p): + Pfmax, Topt, gap, m = p + Tc = Topt + gap + return _tpc(T, Pfmax, Topt, Tc, m) - y + + p0 = [Pfmax0, Topt0, half, m0] + p0 = [min(max(v, l), h) for v, l, h in zip(p0, lo, hi)] + try: + sol = least_squares(residual, p0, bounds=(lo, hi), + method="trf", max_nfev=4000) + Pfmax, Topt, gap, m = sol.x + Tc = Topt + gap + if not np.all(np.isfinite([Pfmax, Topt, Tc, m])) or gap < 1e-9: + raise RuntimeError("degenerate fit") + return {"Pfmax": float(Pfmax), "Topt": float(Topt), + "Tc": float(Tc), "m": float(m)} + except Exception: # noqa: BLE001 — fall back + return {"Pfmax": Pfmax0, "Topt": Topt0, "Tc": Tc0, "m": m0} + + +def predict(X: np.ndarray, Pfmax: float, Topt: float, Tc: float, m: float) -> np.ndarray: + """performance = Pfmax * (1 - x)_+^m * exp(m*x), x = (T-Topt)/(Tc-Topt). + + X: (n, 1) — column 0 is temperature (degrees C). + """ + T = np.asarray(X[:, 0], dtype=float) + return _tpc(T, Pfmax, Topt, Tc, m) diff --git a/tasks/typeII/thermal_performance_curve__pf_utpc/simulator/sample.csv b/tasks/typeII/thermal_performance_curve__pf_utpc/simulator/sample.csv new file mode 100644 index 0000000000000000000000000000000000000000..4820e5e6a14efc27fbd6106dff7706b2715c2572 --- /dev/null +++ b/tasks/typeII/thermal_performance_curve__pf_utpc/simulator/sample.csv @@ -0,0 +1,16001 @@ +group_id,performance,temperature +0,1.471931216335357e-08,15.779387921971646 +0,1.744501903789958e-08,20.23434602119331 +0,1.6223696265564588e-08,18.244760709280165 +0,1.2959580891827924e-08,9.232656990211975 +0,1.2687986166656667e-08,10.459842316795637 +0,1.9075442847946084e-08,19.846992875960364 +0,9.818538410350442e-09,5.63190040716485 +0,1.7830570961876382e-08,18.990358928711622 +0,1.831147917969329e-08,18.59484244587125 +0,1.3940338725416476e-08,13.20645028698569 +0,1.2575761957152453e-08,10.50676507242971 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(1964) Pipe Model Theory, as reviewed in Lehnebach et al. (2018) Annals of Botany 121(5):773-795, PDF pp. 3-4, property 1: A_L = k_p * A_S (leaf area proportional to sapwood cross-sectional area).", + "kind": "reference", + "law_constants": {}, + "local_fittable": [ + "k_p" + ], + "max_fit_seconds": 1.9529834389686584e-05, + "n_clusters_failed": 0, + "n_clusters_fitted": 9, + "other_constants": {}, + "paper_ref": "summary_supporting_lehnebach_2018.md", + "per_cluster": { + "1": { + "log_mae": 0.08483225205673262, + "mae": 22.091919997259026, + "mape": 0.2057037233141469, + "mdae": 7.047342049602388, + "mse": 1436.0289001267834, + "n_finite": 5, + "r2": 0.5212761776154805, + "rmse": 37.89497196366272, + "smape": 0.19386292745606512 + }, + "11": { + "log_mae": 0.218363437086902, + "mae": 103.03011396232112, + "mape": 0.6532751113404501, + "mdae": 29.137072949861476, + "mse": 71959.62822100827, + "n_finite": 36, + "r2": 0.4869884674884992, + "rmse": 268.252918383022, + "smape": 0.4759994992157218 + }, + "13": { + "log_mae": 0.08085183349017189, + "mae": 12.725572940071675, + "mape": 0.20824367173481756, + "mdae": 12.725572940071675, + "mse": 169.4854994909267, + "n_finite": 2, + "r2": 0.46614793507070096, + "rmse": 13.01865966568474, + "smape": 0.18535637592087756 + }, + "15": { + "log_mae": 0.13195732935648008, + "mae": 35.110093830416886, + "mape": 0.37279348652037897, + "mdae": 27.558305904919127, + "mse": 2084.9297320676365, + "n_finite": 4, + "r2": 0.6401325509850233, + "rmse": 45.661030781922086, + "smape": 0.2985250621255572 + }, + "17": { + "log_mae": 0.4077754476009017, + "mae": 13.265033729656674, + "mape": 0.5080210614208269, + "mdae": 11.556401992964414, + "mse": 237.227180564254, + "n_finite": 6, + "r2": 0.4056132902262237, + "rmse": 15.40218103270618, + "smape": 0.7482493704388374 + }, + "3": { + "log_mae": 0.13683183157057582, + "mae": 29.724635634748086, + "mape": 0.4137377287254453, + "mdae": 20.472781125968762, + "mse": 1592.2698003319383, + "n_finite": 5, + "r2": 0.8394470986988575, + "rmse": 39.90325551044599, + "smape": 0.30763585400139665 + }, + "5": { + "log_mae": 0.17887290163262243, + "mae": 7.902812528062692, + "mape": 0.6953119290589257, + "mdae": 7.426075328596444, + "mse": 86.66476866387477, + "n_finite": 18, + "r2": 0.9068909328644741, + "rmse": 9.309391422852235, + "smape": 0.3828763311556228 + }, + "7": { + "log_mae": 0.21092897603318128, + "mae": 15.520845192352052, + "mape": 0.3740132433538177, + "mdae": 15.603550333246066, + "mse": 270.3779421774989, + "n_finite": 4, + "r2": 0.25898895387792065, + "rmse": 16.443173117664937, + "smape": 0.47242337686810404 + }, + "9": { + "log_mae": 0.18035717346184016, + "mae": 120.45671922217714, + "mape": 0.34615384403914967, + "mdae": 88.11120071627377, + "mse": 29068.174406006452, + "n_finite": 9, + "r2": 0.602480632492442, + "rmse": 170.4939131054433, + "smape": 0.4056451451474289 + } + } + } + }, + "derived_caps": { + "fit_timeout_seconds": 10, + "max_init_size_per_param": 1, + "max_law_constants": 1, + "max_local_params": 1 + }, + "metric_declared": "log_mae", + "n_clusters": 9, + "reference_baseline_id": null, + "task": "woody_plant_allometry_baad__a_lf", + "type": "typeII" +} diff --git a/tasks/typeII/woody_plant_allometry_baad__a_lf/eval/validity_rubrics.json b/tasks/typeII/woody_plant_allometry_baad__a_lf/eval/validity_rubrics.json new file mode 100644 index 0000000000000000000000000000000000000000..02f837053db2883497e633961c00ea85fe752768 --- /dev/null +++ b/tasks/typeII/woody_plant_allometry_baad__a_lf/eval/validity_rubrics.json @@ -0,0 +1,11 @@ +{ + "task": "woody_plant_allometry_baad__a_lf", + "validity_rubrics": [ + "Predicted leaf area increases with sapwood cross-sectional area through a pipe-model-style proportional (near-linear) support term: more conductive sapwood area supports proportionally more foliage (Shinozaki Pipe Model Theory, A_L = k_p * A_S)", + "Predicted leaf area scales with supporting woody/conductive tissue as a sub-linear power law with exponent near 3/4 (WBE metabolic fractal-network allometry, Niklas & Enquist 2001, A_L ~ a_ssbh^0.762)", + "Captures the hydraulic-path (tree-height) effect: the leaf-area-to-sapwood-area ratio decreases with plant height, so predicted leaf area is non-increasing with h_t when a_ssbh is held fixed (Whitehead hydraulic extension, A_L/A_S inversely proportional to path length ~ height)", + "Predicted leaf area is non-negative for all valid (positive) inputs", + "Predicted leaf area approaches 0 as sapwood cross-sectional area approaches 0 (zero conductive area supports no foliage; the form passes through the origin)", + "Predicted leaf area is non-decreasing in sapwood cross-sectional area a_ssbh when other inputs are held fixed" + ] +} \ No newline at end of file diff --git a/tasks/typeII/woody_plant_allometry_baad__a_lf/simulator/formula.py b/tasks/typeII/woody_plant_allometry_baad__a_lf/simulator/formula.py new file mode 100644 index 0000000000000000000000000000000000000000..c69bc7c1bda97cc353fe6fcf841d3255d2193ce7 --- /dev/null +++ b/tasks/typeII/woody_plant_allometry_baad__a_lf/simulator/formula.py @@ -0,0 +1,130 @@ +"""Hydraulic-corrected allometric form for whole-plant leaf area (a_lf). + +MEMORIZATION-PROOF VARIANT (sim3 Type II, multi-group). + +This is NOT the textbook pipe-model law (Shinozaki 1964: A_L = k_p * A_S, a +strict linear proportionality with no height term) nor the interspecific 3/4- +power law (Niklas & Enquist 2001: A_L = k * A_S^0.762, a single fixed exponent +with no height term). It is a distinct two-input multiplicative form that +couples a per-group sapwood-area power law to a hydraulic-path (height) +dilution factor: + + A_L = c * A_S^p * H^(-gamma) + +with c, p, gamma all LOCAL_FITTABLE per group (gamma constrained >= 0). + +Physical motivation: + - A_S^p : foliage supported by conductive sapwood. The exponent p is local + (not fixed at 1 or 0.762): it absorbs species-specific deviations between + the pure pipe-model (p=1) and metabolic-scaling (p~3/4) limits caused by + tapering, heartwood formation and bark fraction. + - H^(-gamma) : Whitehead-style hydraulic extension. As the conductive path + length (~ tree height H) grows, hydraulic resistance rises, so the + leaf-area-to-sapwood-area ratio A_L/A_S falls. gamma >= 0 is enforced so + that predicted leaf area is non-increasing in height at fixed sapwood area + (rubric: A_L/A_S inversely related to path length). + +The form is DISTINCT IN FUNCTIONAL SHAPE from either baseline after per-group +fitting: it carries a second predictor (H) that neither baseline uses and a +freely-fitted sapwood exponent. It still passes through the origin in A_S, +is non-negative, and is monotone non-decreasing in A_S. + +Type II — c, p, gamma are LOCAL_FITTABLE per group; the FORM is universal. + +Column mapping (CSV): + A_S -> a_ssbh : sapwood cross-sectional area at breast height (m2). + H -> h_t : total plant height (m). + A_L -> a_lf : whole-plant leaf area (m2). +""" + +import numpy as np + +USED_INPUTS = ["a_ssbh", "h_t"] +PAPER_REF = "summary_supporting_lehnebach_2018.md" +EQUATION_LOC = ( + "Hydraulic-corrected allometry: A_L = c * A_S^p * H^(-gamma). Couples a " + "local sapwood-area power law (Shinozaki pipe-model / Niklas-Enquist " + "scaling limits) to a Whitehead hydraulic-path height dilution; all three " + "parameters fitted per group, gamma constrained non-negative." +) + +LAW_CONSTANTS = {} +OTHER_CONSTANTS = {} +LOCAL_FITTABLE = { + "c": {"init": None}, # per-group normalization (closed-form, log-space) + "p": {"init": None}, # per-group sapwood-area exponent (closed-form) + "gamma": {"init": None}, # per-group height-dilution exponent (>= 0) +} + +# Grid over the (non-negative) hydraulic exponent gamma; c and p are solved in +# closed form by log-space OLS conditional on gamma. +_GAMMA_GRID = np.linspace(0.0, 1.5, 31) + + +def fit(X_fit: np.ndarray, y_fit: np.ndarray) -> dict: + """Fit c, p, gamma per group. + + In log10 space the model is linear: + log10(A_L) = log10(c) + p*log10(A_S) - gamma*log10(H). + gamma is constrained to be non-negative (hydraulic dilution), so we grid + over gamma >= 0 and solve (log c, p) by OLS for each, keeping the least- + squares-best gamma. Robust to thin / degenerate groups. + """ + a_ssbh = np.asarray(X_fit[:, 0], dtype=float) + h_t = np.asarray(X_fit[:, 1], dtype=float) + y = np.asarray(y_fit, dtype=float) + + mask = (a_ssbh > 0) & (h_t > 0) & (y > 0) & \ + np.isfinite(a_ssbh) & np.isfinite(h_t) & np.isfinite(y) + if mask.sum() < 1: + return {"c": 1.0, "p": 1.0, "gamma": 0.0} + + lx = np.log10(a_ssbh[mask]) + lh = np.log10(h_t[mask]) + ly = np.log10(y[mask]) + + # Too few points to fit a slope -> fall back to pure proportionality. + if mask.sum() < 3 or np.ptp(lx) <= 0: + log_c = float(np.mean(ly - lx)) + c = 10.0 ** log_c + if not np.isfinite(c) or c <= 0: + c = 1.0 + return {"c": c, "p": 1.0, "gamma": 0.0} + + A = np.column_stack([np.ones_like(lx), lx]) + best = None + for gamma in _GAMMA_GRID: + rhs = ly + gamma * lh # absorb the -gamma*lh term to the LHS + coef, *_ = np.linalg.lstsq(A, rhs, rcond=None) + pred = A @ coef - gamma * lh + sse = float(np.sum((pred - ly) ** 2)) + if best is None or sse < best[0]: + best = (sse, float(coef[0]), float(coef[1]), float(gamma)) + + _, log_c, p, gamma = best + c = 10.0 ** log_c + + # Guard rails: keep parameters physically sane and finite. + if not np.isfinite(c) or c <= 0: + c = 1.0 + if not np.isfinite(p) or p <= 0: + p = 1.0 + if not np.isfinite(gamma) or gamma < 0: + gamma = 0.0 + return {"c": float(c), "p": float(p), "gamma": float(gamma)} + + +def predict(X: np.ndarray, c: float, p: float, gamma: float) -> np.ndarray: + """A_L = c * A_S^p * H^(-gamma). + + X: (n, 2) — columns [a_ssbh, h_t]. + c : per-group normalization (LOCAL_FITTABLE, > 0). + p : per-group sapwood-area exponent (LOCAL_FITTABLE, > 0). + gamma : per-group height-dilution exponent (LOCAL_FITTABLE, >= 0). + + Non-negative; passes through the origin in a_ssbh; non-decreasing in + a_ssbh; non-increasing in h_t. + """ + a_ssbh = np.clip(np.asarray(X[:, 0], dtype=float), 0.0, None) + h_t = np.clip(np.asarray(X[:, 1], dtype=float), 1e-9, None) + return c * np.power(a_ssbh, p) * np.power(h_t, -gamma) diff --git a/tasks/typeII/woody_plant_allometry_baad__a_lf/simulator/sample.csv b/tasks/typeII/woody_plant_allometry_baad__a_lf/simulator/sample.csv new file mode 100644 index 0000000000000000000000000000000000000000..a740695c3052edd38199a84b5a51449d744a6814 --- /dev/null +++ b/tasks/typeII/woody_plant_allometry_baad__a_lf/simulator/sample.csv @@ -0,0 +1,765 @@ +group_id,a_lf,a_ssbh,h_t +0,4.11523627779964,0.000397,2.16 +0,7.522386187372309,0.001264,4.04 +0,8.342128668187478,0.001418,4.25 +0,9.771481514122657,0.001418,3.89 +0,24.973784437370462,0.001958,4.03 +0,15.139219548950155,0.002666,4.46 +0,14.044074871701184,0.003332,5.67 +0,23.6873879292454,0.005293,6.53 +0,38.710986593360566,0.005405,6.59 +0,51.85851212761373,0.007226,7.26 +0,45.03449867592062,0.008305,7.95 +0,62.21318929002887,0.008432,8.45 +0,65.37947650871455,0.010688,7.83 +0,93.09181063616164,0.012087,8.06 +0,91.9908599490935,0.012822,11.24 +0,72.26570036073693,0.013086,11.39 +0,101.97237093658511,0.01436,9.27 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