| r"""Benchmark metric (identical to the definitions used in the HyperKKL experiments). |
| |
| e_j(t) = xhat_j(t) - x_j(t) |
| sigma_j = reference std of state j (metadata ``x_std``): forced trajectories of the NOMINAL |
| plant at in-distribution inputs after the washout, measured once per plant. Fixed per |
| plant, so every method, tier and setting shares one yardstick. |
| S = settled window: sample indices k >= settle = int(settle_frac * N), settle_frac = 0.5 |
| (metadata ``settle_index``), i.e. the second half of every episode |
| settled NRMSE = sqrt( mean_{k in S} mean_j (e_j(k) / sigma_j)^2 ) per episode |
| NRMSE_j = sqrt( mean_{k in S} (e_j(k) / sigma_j)^2 ) |
| unmeasured NRMSE = mean of NRMSE_j over the unmeasured states (metadata ``unmeasured``) |
| measured NRMSE = mean of NRMSE_j over the measured states (metadata ``sensors``) |
| Every normalised error is clipped to [-100, 100] (non-finite -> 100) before averaging; |
| an episode is flagged diverged if the estimate is non-finite or |e_j / sigma_j| > 100. |
| Report the mean over the episodes of a tier (64 per tier). |
| """ |
| import numpy as np |
|
|
| DIVERGE = 100.0 |
|
|
|
|
| def episode_metrics(x, xh, sigma, settle: int, sensors=None) -> dict: |
| """x, xh: arrays (E, N+1, nx). Returns per-episode arrays (length E).""" |
| x, xh = np.asarray(x, np.float64), np.asarray(xh, np.float64) |
| s = np.asarray(sigma, np.float64) |
| en = (xh - x) / s |
| fin = np.isfinite(xh).all(axis=(1, 2)) |
| with np.errstate(invalid="ignore"): |
| big = (np.abs(en) > DIVERGE).any(axis=(1, 2)) |
| en = np.clip(np.nan_to_num(en, nan=DIVERGE, posinf=DIVERGE, neginf=-DIVERGE), -DIVERGE, DIVERGE) |
| st = en[:, settle:] |
| out = {"nrmse": np.sqrt((st ** 2).mean(axis=(1, 2)))} |
| per = np.sqrt((st ** 2).mean(axis=1)) |
| for j in range(x.shape[-1]): |
| out[f"nrmse_x{j + 1}"] = per[:, j] |
| if sensors is not None: |
| meas = sorted({int(j) for j in sensors}) |
| unm = [j for j in range(x.shape[-1]) if j not in meas] |
| nan = np.full(len(x), np.nan) |
| out["nrmse_measured"] = per[:, meas].mean(-1) if meas else nan |
| out["nrmse_unmeasured"] = per[:, unm].mean(-1) if unm else nan |
| out["diverged"] = ~fin | big |
| return out |
|
|
|
|
| def settled_nrmse(x, xh, meta: dict) -> dict: |
| """Tier-level summary with the plant's metadata: mean settled NRMSE and unmeasured NRMSE.""" |
| m = episode_metrics(x, xh, meta["x_std"], int(meta["settle_index"]), meta["sensors"]) |
| return {"nrmse": float(np.mean(m["nrmse"])), |
| "nrmse_unmeasured": float(np.nanmean(m["nrmse_unmeasured"])), |
| "nrmse_measured": float(np.nanmean(m["nrmse_measured"])), |
| "div_rate": float(np.mean(m["diverged"]))} |
|
|
