Structure-preserving fidelity diagnostics for partial differential equations
Machine learning surrogates of partial differential equations (PDEs) are commonly trained on data generated by numerical solvers. Therefore, the training data obey not the PDE but the modified equation of the numerical scheme, and the test loss, computed on data from the same solver, cannot distinguish a model that learned the physics from one that learned the discretization error. Here, we show that the difference is nevertheless visible in the trained model. We propose a suite of structure-preserving fidelity diagnostics, simple scores that measure whether a learned model respects one known property of the physics, such as a conserved quantity, a symmetry or a Hamiltonian structure, wit...
| Authors | Kyriakos Flouris |
|---|---|
| Primary category | cs.LG |
| Published | 12 October 2026 |
| Last updated at source | 12 October 2026 |
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