01KW05Y7MGBVXXZN8N3YTXJXVJ

Continuity-prior PINN for CSI density — first crush-testbed result (corrected)

Unblock + testbed (C1, met). The python-ml runner (CPU torch, no GPU) is built and runs the PINN in-container. A coupled exp-csi-crowd crowd-size sweep on test-lab-synth — {12,24,36} spread + {60,80} instant-burst (the fix: a spread flow only gave 5 high-rho cell-frames; a burst into a tight funnel + finer binning gives peak rho 4.98 ped/m2, mean 0.80, n=110 high-regime test cell-frames). Coupled artefacts present, no density NaN/Inf.

Estimators (C2, met). Two identical MLPs f(CSI link amplitudes)(t) -> [rho_1..rho_10](t); truth rho + velocity from the trajectory. unconstrained = data MSE; PINN = data MSE + 0.2 * 1D continuity residual (FD closure v(rho)=Weidmann) on the predicted field. Random 70/30 split; continuity loss on the full contiguous sequence.

Result (C3, clauses pass but CONFOUNDED). PINN beats unconstrained in every regime: low (rho<0.5) -6.7%, mid (0.5-1.0) -47.8%, high (rho>=1) -11.1% (RMSE 1.23->1.09), with no loss at low density. Both defeater clauses technically pass. But it is not a clean win, for the reasons the critic established:

• FD-closure circularity (load-bearing). The PINN's Weidmann v(rho) is the same fundamental-diagram family JuPedSim uses to generate the crowd (corpus peak speed ~1.20 m/s). The PINN was effectively handed the generator's velocity law, so the experiment cannot separate "continuity regularizes" from "we leaked the simulator's FD into the loss." No mismatched-FD ablation exists.
• No generic-regularizer baseline. A continuity term is also a smoother; without an L2 / temporal-smoothing / early-stopped control, the gain is not attributable to physics vs regularization. Same-architecture-minus-the-term rules out an architecture confound, not a regularization confound.
• Single seed / single split; -11% has no error bar. The mid-regime -47.8% is over-leveraged (smoothing helps most there; it is not the rho>=1 regime the claim targets). AP-sparsity 0.5 ~ 1.0 is a soft miss vs the di2023 prediction that the prior should help most when sensing is sparse.

Verdict (C4, framing held). A necessary-but-confounded in-silico signal: the prior does lower density RMSE in its valid regime on this testbed, but the FD-closure circularity + missing regularizer baseline + single seed mean this nudges continuity-prior-regularizes-density speculative -> plausible at most, not confirmation. Three named follow-ons convert a fragile win into a real one: (1) a mismatched-FD closure (deliberately wrong v(rho)) — does the gain survive when the prior does NOT match the generator? (2) an L2 / temporal-smoothing baseline — is it physics or just smoothing? (3) multi-seed error bars. Real-channel transfer remains IP-106 / synthetic-csi-sim-to-real-transfer.

Critic (severity: high, disagreed with a clean-WIN reading — corrected above)

Plumbing is clean (artefacts, no density NaN, defeater clauses pass). The interpretation is what fails: this does not earn "supports the central thesis claim."

1. FD-closure circularity (structural). v(rho)=Weidmann is JuPedSim's own FD family; the PINN was told the generative velocity law. The experiment as run cannot separate "continuity regularizes" from "the simulator's FD was leaked into the loss." No mismatched-FD ablation.
2. No fair baseline. Continuity acts as a smoother; without L2/temporal-smoothing/early-stopping controls, the gain is not attributable to physics.
3. Single seed / split: -11.1% high-regime has no error bar; could sit inside seed noise.
4. Mid -47.8% over-leveraged (not the rho>=1 claim regime). AP-sparsity ~flat is a soft miss vs di2023.

Defensible update: speculative -> plausible at most, pending the mismatched-FD ablation + a regularizer baseline + multi-seed. A replan trigger, not a reject.