EKS

.cache/known_methods_snapshot.json

@@ -276,6 +276,41 @@
         "ies-tmcmc",
         "boed-tmcmc"
       ]
+    },
+    "eks": {
+      "abbreviation": "EKS",
+      "Method": "Ensemble Kalman Sampler",
+      "parallelism": "parallel-interacting",
+      "update_type": "gradient (Kalman)",
+      "method_goal": "uq",
+      "emulator_use": "none",
+      "aliases": [
+        "eks",
+        "sampler"
+      ]
+    },
+    "ces-eks": {
+      "abbreviation": "CES-EKS",
+      "Method": "Calibrate Emulate Sample (Ensemble Kalman Sampler)",
+      "parallelism": "parallel-interacting",
+      "update_type": "gradient (Kalman)",
+      "method_goal": "uq",
+      "emulator_use": "after-optimize",
+      "aliases": [
+        "ces-eks"
+      ]
+    },
+    "ies-eks": {
+      "abbreviation": "IES-EKS",
+      "Method": "Iterated Emulate-Sample (EKS)",
+      "parallelism": "parallel-interacting",
+      "update_type": "general",
+      "method_goal": "uq",
+      "emulator_use": "within-optimize",
+      "aliases": [
+        "ies-eks",
+        "boed-eks"
+      ]
     }
   },
   "observed_methods": [

CLAUDE.md

@@ -83,7 +83,9 @@ calibration_benchmark/
 │   ├── rl-td3/                  RL-TD3-SHORT / RL-TD3 (TD3 variant of the RL experiments; RL-TD3 files are `rl-td3-long` in the NetCDF) results (per-benchmark files)
 │   ├── rl-ddpg/                 RL-DDPG-SHORT / RL-DDPG (DDPG actor-critic; short RL step / standard-window RL step; RL-DDPG files are `rl-ddpg-long` in the NetCDF) results (per-benchmark files)
 │   ├── ces-eki-dmc_results/     CES-EKI-DMC ensemble-results files (UQ source)
-│   ├── gboed-uq_results/        GBOED ensemble-results files (UQ source; 2026-10-16 GBOED-TMCMC/IES-TMCMC and 2026-10-19 IEKF-based variants, all four benchmarks; files are named `boed-*`: `tmcmc-eig` = GBOED-TMCMC, `iekf-eig` = GBOED-IEKF, `iekf` = IES-IEKF, `tmcmc` = IES-TMCMC; IES = Iterated Emulate-Sample)
+│   ├── gboed-uq_results/        GBOED ensemble-results files (UQ source; 2026-10-16 GBOED-TMCMC/IES-TMCMC and 2026-10-19 IEKF-based variants, all four benchmarks; files are named `boed-*`: `tmcmc-eig` = GBOED-TMCMC, `iekf-eig` = GBOED-IEKF, `iekf` = IES-IEKF, `tmcmc` = IES-TMCMC, `eks` = IES-EKS (2026-10-30), `eks-eig` = GBOED-EKS (2026-11-01); IES = Iterated Emulate-Sample)
+│   ├── ces-eks_results/         CES-EKS ensemble-results files (UQ source; 2026-10-29, all four benchmarks)
+│   ├── eks_results/             EKS (Ensemble Kalman Sampler) ensemble-results files (UQ source; 2026-10-28, all four benchmarks; files are named `leaderboard_sampler_*`)
 │   ├── gnki-uq_results/         IEKF (a.k.a GNKI) ensemble-results files (UQ source)
 │   └── abc/                     ABC ensemble-results files (UQ source; per-benchmark files)
 ├── offline-plots/               leaderboard_plot.py — matplotlib replica of the leaderboard charts
@@ -220,6 +222,10 @@ A quick taxonomy tree is rendered on the home page (`src/streamlit_app.py`).
 | `ies-iekf` | IES-IEKF | parallel-interacting | general | uq | within-optimize | boed-iekf |
 | `gboed-iekf` | GBOED-IEKF | parallel-interacting | general | uq | within-optimize | gboed-iekf-eig, boed-iekf-eig |
 | `ies-tmcmc` | IES-TMCMC | parallel-interacting | general | uq | within-optimize | boed-tmcmc |
+| `eks` | EKS | parallel-interacting | gradient (Kalman) | uq | none | sampler |
+| `ces-eks` | CES-EKS | parallel-interacting | gradient (Kalman) | uq | after-optimize | — |
+| `ies-eks` | IES-EKS | parallel-interacting | general | uq | within-optimize | boed-eks |
+| `gboed-eks` | GBOED-EKS | parallel-interacting | general | uq | within-optimize | gboed-eks-eig, boed-eks-eig |
 | `lm-kgmm` | LM-KGMM | serial | gradient (score) | optimization | none | — |
 | `lm-dsm` | LM-DSM | serial | gradient (score) | optimization | none | — |
 | `adam-kgmm` | ADAM-KGMM | serial | gradient (score) | optimization | none | — |

data/ces-eks_results/ces-eks-pca_l63_ensemble_results_2026-10-30_minimal.nc

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data/ces-eks_results/ces-eks-pca_l96_ensemble_results_2026-10-30_minimal.nc

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data/ces-eks_results/ces-eks-pca_l96_spatial_forcing_ensemble_results_2026-10-30_minimal.nc

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data/eks_results/leaderboard_sampler_l96_flux-force_2026-10-28_minimal.nc

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data/eks_results/leaderboard_sampler_l96_vec-force_2026-10-28_minimal.nc

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data/gboed-uq_results/boed-eks-eig_l63_ensemble_results_2026-11-01_minimal.nc

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data/gboed-uq_results/boed-eks-eig_l96_const-force_2026-11-01_minimal.nc

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data/gboed-uq_results/boed-eks-eig_l96_flux-force_2026-11-01_minimal.nc

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data/gboed-uq_results/boed-eks-eig_l96_vec-force_2026-11-01_minimal.nc

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data/gboed-uq_results/boed-eks_l63_ensemble_results_2026-10-30_minimal.nc

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src/common/method_registry.py

@@ -264,6 +264,42 @@ KNOWN_METHODS = {
         "emulator_use": "within-optimize",
         "aliases": ["ies-tmcmc", "boed-tmcmc"],
     },
+    "eks": {
+        "abbreviation": "EKS",
+        "Method": "Ensemble Kalman Sampler (EKS a.k.a ALDI)",
+        "parallelism": "parallel-interacting",
+        "update_type": "gradient (Kalman)",
+        "method_goal": "uq",
+        "emulator_use": "none",
+        "aliases": ["eks", "sampler"],
+    },
+    "ces-eks": {
+        "abbreviation": "CES-EKS",
+        "Method": "Calibrate Emulate Sample (EKS)",
+        "parallelism": "parallel-interacting",
+        "update_type": "gradient (Kalman)",
+        "method_goal": "uq",
+        "emulator_use": "after-optimize",
+        "aliases": ["ces-eks"],
+    },
+    "ies-eks": {
+        "abbreviation": "IES-EKS",
+        "Method": "Iterated Emulate-Sample (EKS)",
+        "parallelism": "parallel-interacting",
+        "update_type": "general",
+        "method_goal": "uq",
+        "emulator_use": "within-optimize",
+        "aliases": ["ies-eks", "boed-eks"],
+    },
+    "gboed-eks": {
+        "abbreviation": "GBOED-EKS",
+        "Method": "Goal-oriented Bayesian Optimal Experimental Design (EKS)",
+        "parallelism": "parallel-interacting",
+        "update_type": "general",
+        "method_goal": "uq",
+        "emulator_use": "within-optimize",
+        "aliases": ["gboed-eks", "gboed-eks-eig", "boed-eks-eig"],
+    },
 }
 
 
@@ -326,13 +362,13 @@ METHOD_COLORS: dict[str, str] = {
 # family.  A family only appears on a board if one of its methods has data there.
 # Every method that can appear in a suitability table must be listed here.
 SUITABILITY_FAMILIES: dict[str, list[str]] = {
-    "CES": ["CES-EKI-CONST", "CES-EKI-DMC", "CES-IEKF-CONST"],
-    "Kalman": ["ETKI", "IEKF", "TEKI", "UKI"],
+    "CES": ["CES-EKI-CONST", "CES-EKI-DMC", "CES-EKS", "CES-IEKF-CONST"],
+    "Kalman": ["EKS", "ETKI", "IEKF", "TEKI", "UKI"],
     "Gradient": ["LM", "ADAM"],
     "GFDT": ["LM-DSM", "ADAM-DSM", "LM-KGMM", "ADAM-KGMM"],
     "RL": ["RL-DDPG", "RL-TD3", "RL-DDPG-SHORT", "RL-TD3-SHORT"],
-    "IES": ["IES-IEKF", "IES-TMCMC"],
-    "GBOED": ["GBOED-IEKF", "GBOED-TMCMC"],
+    "IES": ["IES-EKS", "IES-IEKF", "IES-TMCMC"],
+    "GBOED": ["GBOED-EKS", "GBOED-IEKF", "GBOED-TMCMC"],
     "General": ["ABC", "HM"],
 }
 

src/data_store.py

@@ -135,7 +135,11 @@ UQ_BUDGET_FILES: dict[str, list[tuple[str, str]]] = {
         ("ies-iekf", "gboed-uq_results/boed-iekf_l63_ensemble_results_2026-10-19_minimal.nc"),
         ("gboed-iekf", "gboed-uq_results/boed-iekf-eig_l63_ensemble_results_2026-10-19_minimal.nc"),
         ("ies-tmcmc", "gboed-uq_results/boed-tmcmc_l63_ensemble_results_2026-10-16_minimal.nc"),
+        ("ies-eks", "gboed-uq_results/boed-eks_l63_ensemble_results_2026-10-30_minimal.nc"),
+        ("gboed-eks", "gboed-uq_results/boed-eks-eig_l63_ensemble_results_2026-11-01_minimal.nc"),
         ("abc", "abc/leaderboard_abc_l63_2026-09-10_minimal.nc"),
+        ("eks", "eks_results/leaderboard_sampler_l63_2026-10-28_minimal.nc"),
+        ("ces-eks", "ces-eks_results/ces-eks-pca_l63_ensemble_results_2026-10-30_minimal.nc"),
     ],
     "L96":                [
         ("ces-eki-dmc", "ces-eki-dmc_results/ces-eki-dmc_l96_ensemble_results_2026-06-15_minimal.nc"),
@@ -147,7 +151,11 @@ UQ_BUDGET_FILES: dict[str, list[tuple[str, str]]] = {
         ("ies-iekf", "gboed-uq_results/boed-iekf_l96_const-force_2026-10-19_minimal.nc"),
         ("gboed-iekf", "gboed-uq_results/boed-iekf-eig_l96_const-force_2026-10-19_minimal.nc"),
         ("ies-tmcmc", "gboed-uq_results/boed-tmcmc_l96_const-force_2026-10-16_minimal.nc"),
+        ("ies-eks", "gboed-uq_results/boed-eks_l96_const-force_2026-10-30_minimal.nc"),
+        ("gboed-eks", "gboed-uq_results/boed-eks-eig_l96_const-force_2026-11-01_minimal.nc"),
         ("abc", "abc/leaderboard_abc_l96_const-force_2026-09-10_minimal.nc"),
+        ("eks", "eks_results/leaderboard_sampler_l96_const-force_2026-10-28_minimal.nc"),
+        ("ces-eks", "ces-eks_results/ces-eks-pca_l96_ensemble_results_2026-10-30_minimal.nc"),
     ],
     "L96_NN_FORCING":     [
         ("ces-eki-dmc", "ces-eki-dmc_results/ces-eki-dmc_l96_nn_forcing_ensemble_results_2026-06-15_minimal.nc"),
@@ -159,7 +167,11 @@ UQ_BUDGET_FILES: dict[str, list[tuple[str, str]]] = {
         ("ies-iekf", "gboed-uq_results/boed-iekf_l96_flux-force_2026-10-19_minimal.nc"),
         ("gboed-iekf", "gboed-uq_results/boed-iekf-eig_l96_flux-force_2026-10-19_minimal.nc"),
         ("ies-tmcmc", "gboed-uq_results/boed-tmcmc_l96_flux-force_2026-10-16_minimal.nc"),
+        ("ies-eks", "gboed-uq_results/boed-eks_l96_flux-force_2026-10-30_minimal.nc"),
+        ("gboed-eks", "gboed-uq_results/boed-eks-eig_l96_flux-force_2026-11-01_minimal.nc"),
         ("abc", "abc/leaderboard_abc_l96_flux-force_2026-09-10_minimal.nc"),
+        ("eks", "eks_results/leaderboard_sampler_l96_flux-force_2026-10-28_minimal.nc"),
+        ("ces-eks", "ces-eks_results/ces-eks-pca_l96_nn_forcing_ensemble_results_2026-11-01_minimal.nc"),
     ],
     "L96_SPATIAL_FORCING": [
         ("ces-eki-dmc", "ces-eki-dmc_results/ces-eki-dmc_l96_spatial_forcing_ensemble_results_2026-06-15_minimal.nc"),
@@ -171,7 +183,11 @@ UQ_BUDGET_FILES: dict[str, list[tuple[str, str]]] = {
         ("ies-iekf", "gboed-uq_results/boed-iekf_l96_vec-force_2026-10-19_minimal.nc"),
         ("gboed-iekf", "gboed-uq_results/boed-iekf-eig_l96_vec-force_2026-10-19_minimal.nc"),
         ("ies-tmcmc", "gboed-uq_results/boed-tmcmc_l96_vec-force_2026-10-16_minimal.nc"),
+        ("ies-eks", "gboed-uq_results/boed-eks_l96_vec-force_2026-10-30_minimal.nc"),
+        ("gboed-eks", "gboed-uq_results/boed-eks-eig_l96_vec-force_2026-11-01_minimal.nc"),
         ("abc", "abc/leaderboard_abc_l96_vec-force_2026-09-10_minimal.nc"),
+        ("eks", "eks_results/leaderboard_sampler_l96_vec-force_2026-10-28_minimal.nc"),
+        ("ces-eks", "ces-eks_results/ces-eks-pca_l96_spatial_forcing_ensemble_results_2026-10-30_minimal.nc"),
     ],
 }
 

src/pages/MethodDetails.py

@@ -258,6 +258,41 @@ method_meta = {
         ],
         "notes": "Same after-optimize emulator caveat as CES-EKI-DMC, with the Gauss-Newton calibrate step's usual small-ensemble sensitivity (see IEKF).",
     },
+    "CES-EKS": {
+        "citation": "Cleary et al., J. Comput. Phys., 2021; Garbuno-Inigo, Nüsken and Reich, SIAM J. Appl. Dyn. Syst., 2020",
+        "url": "https://doi.org/10.1016/j.jcp.2020.109716",
+        "source": "`uq_experiments/calibrate_emulate_sample` — `CALIBRATE_METHOD=eks` (calibrate stage `Sampler(prior)` + `EKSStableScheduler()`), `DIM_REDUCTION=PCA` (leaderboard key `ces-eks-pca`).",
+        "math": (
+            "Calibrate-Emulate-Sample whose calibrate stage runs the Ensemble Kalman Sampler (see the EKS entry) instead of "
+            "plain EKI. Calibrate: run the sampler to generate `(θ, G(θ))` training pairs; iteration `k` trains on "
+            "the pairs from the first `k` steps. Emulate: fit a scalar random-feature surrogate `Ĝ(θ)` on those "
+            "pairs. Sample: draw from `π(θ|y) ∝ exp(-½‖y-Ĝ(θ)‖²_Γ)·π(θ)` against the cheap surrogate using "
+            "preconditioned Crank-Nicolson Metropolis-Hastings (pCN-MH), rather than the true forward model."
+        ),
+        "guardrails": (
+            "Calibrate stage: `Sampler(prior)` with the data-dependent `EKSStableScheduler()`. The random-feature "
+            "kernel has a `1e-6` diagonal nugget. The nullspace-noise injector is switched off for this variant, so directions dropped by the "
+            "input PCA are decoded at the prior mean rather than filled with prior noise (the experiment config "
+            "notes that injecting noise inflated the posterior on L96 flux-force, with output spread about 2x too "
+            "wide and no contraction with `k`). Sample stage auto-tunes the pCN step size (`optimize_stepsize`, "
+            "2,000-sample dry run) before the full chain."
+        ),
+        "params": [
+            {"Parameter": "calibrate sampler / scheduler", "Value": "Sampler(prior) / EKSStableScheduler()"},
+            {"Parameter": "n_features / n_features_opt", "Value": "100/60 (L63), 200/160 (L96 variants)"},
+            {"Parameter": "kernel nugget", "Value": "1e-6"},
+            {"Parameter": "MCMC samples / burn-in", "Value": "100,000 / 2,000 (pCN-MH)"},
+            {"Parameter": "init_stepsize", "Value": "0.2 (L63) / 0.01 (L96), auto-tuned before the full chain"},
+            {"Parameter": "nullspace noise injector", "Value": "off (threshold Inf)"},
+        ],
+        "notes": (
+            "The emulator is fit once per iteration `k` on the sampler's first `k` steps, so quality depends on "
+            "how well the calibrate-stage ensemble covers the posterior region. In the current UQ data "
+            "(c = 1.5, best reliable ensemble size) the mean budget is 5.3 on L63, 6.0 on L96 const-force, 87.5 "
+            "on vec-force (0% failures) and 207 on NN flux-force, which fails on at least 5% of seeds at every "
+            "size (15% at the best one)."
+        ),
+    },
     "ADAM": {
         "citation": "Kingma & Ba, ICLR, 2015",
         "url": "https://doi.org/10.48550/arXiv.1412.6980",
@@ -667,6 +702,124 @@ method_meta = {
             "(vec-force and NN flux-force) it fails on at least 35% and 40% of seeds, respectively, at every ensemble size."
         ),
     },
+    "EKS": {
+        "citation": "Garbuno-Inigo, Nüsken and Reich, SIAM J. Appl. Dyn. Syst., 2020 (ALDI); Garbuno-Inigo, Hoffmann, Li and Stuart, SIAM J. Appl. Dyn. Syst., 2020 (original EKS)",
+        "url": "https://doi.org/10.1137/19M1304891",
+        "source": "`uq_experiments/KalmanSampler` — `calibrate_l63.jl`/`calibrate_l96.jl`, `experiment_config.jl` (`METHOD=sampler`, leaderboard key `sampler`); `EKP.Sampler(prior)` with EnsembleKalmanProcesses' default `sampler_type = \"aldi\"`.",
+        "math": (
+            "EKS (a.k.a ALDI): the Ensemble Kalman Sampler in its affine-invariant Langevin form (ALDI). It is a "
+            "derivative-free interacting-particle system that approximately samples the posterior. Each iteration "
+            "moves every member with an ensemble-Kalman drift (parameter/output ensemble covariances stand in for "
+            "a simulator Jacobian), a prior term applied implicitly, a finite-sample correction `(d+1)/J` times "
+            "the member's deviation from the ensemble mean, and noise built from the ensemble square root. Unlike "
+            "EKI the noise keeps the ensemble from collapsing, so the ensemble approximates the posterior rather "
+            "than a point estimate. There is no emulator: the ensemble at each iteration is itself the posterior "
+            "estimate."
+        ),
+        "math_eq": r"\theta^{(j)}_{n+1} = \left(I + \Delta t_n C_n \Gamma_\theta^{-1}\right)^{-1}\left[\theta^{(j)}_n - \frac{\Delta t_n}{J}\sum_{k=1}^J \langle \mathcal{G}(\theta^{(k)}_n) - \bar{\mathcal{G}}_n,\, \Gamma_y^{-1}(\mathcal{G}(\theta^{(j)}_n) - y)\rangle (\theta^{(k)}_n - \bar\theta_n) + \Delta t_n C_n \Gamma_\theta^{-1} m_\theta + \Delta t_n \frac{d+1}{J}(\theta^{(j)}_n - \bar\theta_n)\right] + \sqrt{\frac{2\Delta t_n}{J}}\sum_{k=1}^J \xi_{jk}\,(\theta^{(k)}_n - \bar\theta_n)",
+        "guardrails": (
+            "The step size comes from `EKSStableScheduler()` (numerator 1, nugget `eps()`), so it is adaptive and "
+            "data-dependent, `Δt = 1/(‖D‖ + eps)` with `D` the ensemble-weighted data-misfit matrix, and needs "
+            "no hand-tuned schedule."
+        ),
+        "params": [
+            {"Parameter": "sampler_type", "Value": "\"aldi\" (EKP default)"},
+            {"Parameter": "scheduler", "Value": "EKSStableScheduler() (numerator 1, nugget eps())"},
+        ],
+        "notes": (
+            "**No emulator and no MCMC; each iteration costs `N_ens` forward runs.** In the current UQ data "
+            "(c = 1.5, best reliable ensemble size) it needs a mean budget of 4.2 on L63 (15% failures) and 4.2 "
+            "on L96 const-force, taking only about one iteration. On the two high-dimensional cases it needs "
+            "7 to 8 iterations, so the budget grows with ensemble size: 353 at size 50 on NN flux-force and "
+            "460 at size 55 on vec-force (5% failures each); the largest sizes fail on up to 25-30% of seeds."
+        ),
+    },
+    "IES-EKS": {
+        "citation": "Elsaesser et al., J. Adv. Model. Earth Syst., 2025; Garbuno-Inigo, Hoffmann, Li and Stuart, SIAM J. Appl. Dyn. Syst., 2020 (EKS)",
+        "url": "https://doi.org/10.1029/2024MS004713",
+        "source": "`uq_experiments/BayesianOptimalExperimentalDesign` — `boed_core.jl` (`run_eks`, `acquire_batch`), variant `:eks` (leaderboard key `boed-eks`); `experiment_config.jl` sets `eks_sampler_type = \"eks\"`.",
+        "math": (
+            "The same iterated emulate-sample loop as IES-IEKF and IES-TMCMC (see those entries), with the "
+            "posterior sampler swapped for the Ensemble Kalman Sampler (EKP `Sampler`). Iteration 1 "
+            "forward-evaluates an `N_ens`-point Latin-hypercube design in the truncated, prior-whitened space. "
+            "Each later iteration: (i) refits one GP per whitened output mode on all `(θ, G(θ))` pairs so far; "
+            "(ii) draws an approximate posterior by running the sampler on the GP-mean forward map (no true "
+            "forward evaluations), from a 200-member Latin-hypercube standard-normal start with the prior "
+            "N(0, I) and identity noise; (iii) takes the next `N_ens` forward-model evaluation points as a random "
+            "subsample of that ensemble."
+        ),
+        "guardrails": (
+            "The sampler is `EKP.Sampler` with `sampler_type = \"eks\"` (the original EKS of Garbuno-Inigo, "
+            "Hoffmann, Li and Stuart, not the ALDI variant used by the EKS and CES-EKS entries), driven by "
+            "`EKSStableScheduler(alpha = 0.25)` for a fixed 500 steps. `alpha = 0.25` was chosen because it "
+            "sat closer to the ST-MCMC reference than the default 1, and `alpha >= 3` is unstable. Like the IEKF "
+            "variant it ignores the GP predictive variance. GP fits use the same data-relative hyperparameter "
+            "bounds and iteration caps as IES-IEKF. The posterior has 200 draws rather than 1000; the "
+            "shortfall is padded with NaN rows that the leaderboard stage drops."
+        ),
+        "params": [
+            {"Parameter": "sampler_type", "Value": "\"eks\" (original EKS)"},
+            {"Parameter": "EKS particles (eks_n_particles)", "Value": "200"},
+            {"Parameter": "scheduler", "Value": "EKSStableScheduler(alpha = 0.25)"},
+            {"Parameter": "steps (eks_max_iters / eks_T)", "Value": "500 / Inf (fixed step count)"},
+            {"Parameter": "batch size per iteration", "Value": "N_ens (random subsample of the EKS ensemble)"},
+            {"Parameter": "gp_optim_iters / gp_outer_iters", "Value": "50 / 3"},
+        ],
+        "notes": (
+            "**Cheap in forward runs but with a fixed 500-step sampler cost per iteration** (GP-mean evaluations "
+            "only). In the current UQ data (c = 1.5, best ensemble size) its mean budget is 5.4 on L63, 4.2 on "
+            "L96 const-force and 112 on NN flux-force (size 80), all with 0% failures. On vec-force it fails on "
+            "at least 20% of seeds at every ensemble size, so it is not suitable there under the 20% threshold."
+        ),
+    },
+    "GBOED-EKS": {
+        "citation": "Holthuijzen et al. 2026 (EIG acquisition); Garbuno-Inigo, Hoffmann, Li and Stuart, SIAM J. Appl. Dyn. Syst., 2020 (EKS posterior sampler)",
+        "url": "https://arxiv.org/abs/2508.13071",
+        "source": "`uq_experiments/BayesianOptimalExperimentalDesign` — `boed_core.jl` (`run_eks`, `optimize_batch`, `acquire_batch`), variant `:eks_eig` (leaderboard key `boed-eks-eig`); `experiment_config.jl` sets `eks_sampler_type = \"eks\"`.",
+        "math": (
+            "GBOED with the posterior sampler swapped for the Ensemble Kalman Sampler (see the GBOED-IEKF and "
+            "IES-EKS entries). Iteration 1 forward-evaluates an `N_ens`-point Latin-hypercube design in the "
+            "truncated prior-whitened space. Each later iteration: (i) refits one GP per whitened output mode on "
+            "all `(θ, G(θ))` pairs so far; (ii) draws an approximate posterior by running the sampler on the "
+            "GP-mean forward map (no true forward evaluations); (iii) chooses the next `N_ens` evaluation "
+            "points by jointly maximizing the closed-form Expected Information Gain (EIG) of the whole batch "
+            "against a 50-member random subsample of the EKS ensemble, starting from a random subsample of "
+            "the full ensemble."
+        ),
+        "math_eq": r"\mathrm{EIG}(X) = \frac{1}{k}\sum_j \frac{1}{2}\log\frac{\det K_{pp}^{(j)}}{\det \Sigma'^{(j)}}, \quad \Sigma'^{(j)} = K_{pp}^{(j)} - K_{pc}^{(j)}\left(K_{cc}^{(j)}\right)^{-1}K_{cp}^{(j)}",
+        "guardrails": (
+            "The sampler is `EKP.Sampler` with `sampler_type = \"eks\"` (original EKS, not ALDI), run for a "
+            "fixed 500 steps of `EKSStableScheduler(alpha = 0.25)` with 200 particles, ignoring the GP "
+            "predictive variance. The batch is optimized with `Optim.jl`'s `LBFGS` inside the χ² ball of the "
+            "prior-whitened space (radial `tanh` squash, so every candidate has radius below √χ²_k(0.999)), with "
+            "a hard cap on raw EIG evaluations (`eig_call_limit`) and an outer-iteration cap "
+            "(`eig_outer_iters`), logging a warning that the returned batch may be \"under-optimized\" if either "
+            "is hit; a diagonal jitter (`eig_jitter`, relative to the GP signal variance) stabilizes the "
+            "covariance solves and log-determinants. GP fits use the same data-relative bounds and iteration "
+            "caps as IES-IEKF."
+        ),
+        "params": [
+            {"Parameter": "sampler_type", "Value": "\"eks\" (original EKS)"},
+            {"Parameter": "EKS particles (eks_n_particles)", "Value": "200"},
+            {"Parameter": "scheduler", "Value": "EKSStableScheduler(alpha = 0.25)"},
+            {"Parameter": "steps (eks_max_iters / eks_T)", "Value": "500 / Inf (fixed step count)"},
+            {"Parameter": "n_eig_posterior_samples (EIG subsample X')", "Value": "50"},
+            {"Parameter": "eig_region / eig_ball_quantile", "Value": ":ball / 0.999 (χ² ball in prior-whitened space)"},
+            {"Parameter": "eig_optim_iters / eig_outer_iters", "Value": "500 / 20"},
+            {"Parameter": "eig_call_limit", "Value": "2000 EIG evaluations"},
+            {"Parameter": "eig_g_tol / eig_f_reltol", "Value": "1e-3 / 1e-6"},
+            {"Parameter": "eig_jitter", "Value": "1e-6 × GP signal variance"},
+            {"Parameter": "gp_optim_iters / gp_outer_iters", "Value": "50 / 3"},
+            {"Parameter": "batch_init_strategy", "Value": ":posterior_subsample"},
+        ],
+        "notes": (
+            "**Adds the EIG batch optimization to IES-EKS**, so it pays for the inner EIG-maximization loop on "
+            "top of the 500-step sampler; hitting its call or outer-iteration limits gives \"under-optimized\" "
+            "batches. In the current UQ data (c = 1.5, best ensemble size) its mean budget is 5.2 on L63, 4.2 on "
+            "L96 const-force and 105 on NN flux-force (size 80, 5% failures). On vec-force it fails on at least "
+            "25% of seeds at every ensemble size, so it is not suitable there under the 20% failure threshold."
+        ),
+    },
     "GBOED-IEKF": {
         "citation": "Holthuijzen et al. 2026 (EIG acquisition); IEKF posterior sampler replaces ST-MCMC",
         "url": "https://arxiv.org/abs/2508.13071",