arXiv:2506. 20181v2 Announce Type: replace Abstract: We study operator relevance in data-driven partial differential equation (PDE) discovery.
Summary generated by The Flow from the publisher's feed. The full article lives at arXiv Machine Learning.
arXiv:2605. 26631v2 Announce Type: replace-cross Abstract: We propose KO-PDE-IDENT, a data-driven framework for identifying parsimonious partial differential equations (PDEs) with false discovery rate (FDR) control.
arXiv:2606. 04804v1 Announce Type: new Abstract: Generative models -- diffusion and flow matching -- are increasingly used to solve partial differential equation (PDE) inverse problems, enforcing the governing physics as a \emph{hard constraint} (via projection or guidance) and reporting the resulting samples as a Bayesian posterior with calibrated uncertainty.
arXiv:2607. 10546v1 Announce Type: new Abstract: Discovering governing partial differential equations (PDEs) from noisy observational data is a fundamental challenge in scientific machine learning.
Generative models -- diffusion and flow matching -- are increasingly used to solve partial differential equation (PDE) inverse problems, enforcing the governing physics as a \emph{hard constraint} (via projection or guidance) and reporting the resulting samples as a Bayesian posterior with calibrated uncertainty. We show that this widely adopted recipe samples the wrong distribution.
arXiv:2608. 05702v1 Announce Type: new Abstract: Scientific machine learning commonly validates models at the level of a subdomain, a benchmark split, or an explanation for one prediction.
arXiv:2607. 23753v1 Announce Type: new Abstract: Partial differential equation (PDE) discovery aims to identify from data the governing law of a physical system.