Do Neural PDE Solvers Learn the Right Dynamics?
Neural PDE solvers can achieve low prediction errors, but do they reproduce the dynamics of the systems they model? Prediction scores alone offer an incomplete answer: they measure agreement with reference solutions but provide limited insight into how errors accumulate, nearby states diverge, or extreme events arise. We propose an evaluation framework that directly examines these behaviors in deterministic and stochastic neural solvers. By evolving ensembles of nearby initial states and comparing them with direct numerical simulation, we assess three complementary aspects of learned dynamics: error formation, ensemble geometry, and extreme events. Experiments on two-dimensional Kolmogoro...
| Authors | Haonan Li, Yue Song, Bin Yang et al. |
|---|---|
| Primary category | cs.LG |
| Published | 3 October 2026 |
| Last updated at source | 3 October 2026 |
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