Accuracy–Consistency Tradeoffs in Conservation-Constrained and Progressive-Cap PINNs for Inverse Source Identification

Abstract

This work contributes an auditable benchmark and gate-based evaluation protocol, rather than a new physics-informed neural network (PINN) variant, for inverse source identification. The benchmark tests whether inverse accuracy, residual consistency, optimization adequacy, and identifiability agree in a one-dimensional advection–diffusion–reaction problem. Its core design contains 560 predeclared confirmatory runs over mass balance, a progressive time-domain cap, and residual-adaptive refinement (RAR), compared with 75 runs in the preliminary ablation reported in an earlier version of this manuscript. Post-escalation convergence is verified on a frozen $3201\times 3201$ truth grid. A normalized multistart finite-difference (FD)–Tikhonov inverse baseline, temporal-mode audit, forward-oracle and optimizer studies, loss-weight/Pareto confirmation, Fisher/profile analysis, and source-width mismatch suite provide external and mechanistic calibration. At nominal 5% noise, the progressive-cap-only configuration attains the lowest median source-center error (0.01808), whereas the mass-constrained RAR configuration attains the lowest common-grid mass residual (2.046e-05). The principal supported conclusion is bounded: A robust inverse-accuracy versus residual-consistency trade-off is confirmed across held-out weight configurations. The width-mismatch suite identifies statistically robust degradation and bounds the conclusions to model-consistent or modestly misspecified Gaussian sources. The held-out inverse-gradient RAR intervention does not satisfy the predeclared contribution rule.