Reference-Free Trust Indicators for Neural PDE Surrogates: A Controlled Comparison Against an Input-Only Null

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I compare three reference-free trust indicators for neural PDE surrogates (the PDE residual, ensemble disagreement, and a probe on frozen internal features) against a null model computed from the initial condition alone. In a preregistered test, none of the three beats the input-only null. On this benchmark, surrogate error ranks largely with how far the true solution travels from its input, which the input already determines. The physics-informed surrogates did not learn the dynamics under the recipe used, which is reported as a negative result. Code and full audit trail: https://github.com/Sankalp895/surrogate-trust-audit