On the post-hoc Evaluation of PDE Discovery: A Multifaceted Challenge of Scientific Advancement
Partial differential equation (PDE) discovery aims to identify from data the governing law of a physical system. Constituting a cornerstone of scientific advancement, it has become during the past decade a major line of research in the rapidly evolving field of Physics-informed Machine Learning (PiML). Among the remaining open problems to address in this domain, the post-hoc evaluation of discovered PDEs raises the particular difficulty of being multifaceted. Indeed, it requires jointly considering predictive accuracy, physical consistency, interpretability, and out-of-distribution generalization capacity. Given that some of these properties are conflicting, it is worth noting that the wi...
| Authors | Baptiste Mathevon, Farah Cherfaoui, Amaury Habrard et al. |
|---|---|
| Primary category | cs.LG |
| Published | 26 July 2026 |
| Last updated at source | 26 July 2026 |
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