Wrong Operator or Blind Design? A Reference-Free Diagnostic for Physics-Informed Coefficient Learning

תקציר מקורי באנגליתarXiv:2608.16925v2 Announce Type: replace Abstract: Physics-informed neural networks and hybrid models infer PDE coefficients from noisy data. When a trained network returns one, no standard check says whether to trust it. We show what those checks report when the operator is wrong: one sensor aggregating several diffusion sources. On one parabolic benchmark at $2\%$ noise, the in-domain error is $1.4$ times the noise while the identified diffusivity settles $30\%$ off. Every least-squares minimiser reaches that value, which drifts $27\%$ across windows; the network, whose objective is composite, settles $1.3\%$ away. The checks stay as silent when the design is blind to a rate of a richer operator, though the remedies are opposite. We develop a reference-free diagnostic, read in the physi