arXiv:2607. 29665v1 Announce Type: new Abstract: PDE discovery from sparse observations requires reconstructing a continuous field and selecting the correct differential terms.
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.
arXiv:2606. 27354v1 Announce Type: cross Abstract: Neural surrogate models offer fast approximate mappings from PDE parameters to solutions, but they typically treat solving as a purely statistical task: once trained, they struggle to correct their own constraint violations and extrapolate beyond the training distribution.
arXiv:2606. 17460v1 Announce Type: new Abstract: Neural operators are widely used as surrogate solution maps for partial differential equations (PDEs), but full-size models can be costly to store, deploy, and evaluate in many-query scientific workflows.
arXiv:2602. 12706v2 Announce Type: replace Abstract: Neural operators have emerged as fast surrogate solvers for parametric partial differential equations (PDEs).
arXiv:2606. 30699v1 Announce Type: new Abstract: Discovering governing equations directly from observational data is a key step towards interpretable scientific machine learning.
arXiv:2607. 14233v1 Announce Type: cross Abstract: Physics-informed neural networks (PINNs) have had a broad research impact in modeling domains governed by partial differential equations (PDE).
arXiv:2607. 22215v1 Announce Type: new Abstract: In this study, we introduce latent PDE mapping, a broadly applicable physics-informed learning technique designed to enable efficient geometric generalization with sparse training data.
arXiv:2606. 00988v1 Announce Type: new Abstract: Symbolic regression (SR) offers a route to scientific discovery by converting observations into interpretable governing equations.
arXiv:2606. 09949v1 Announce Type: cross Abstract: Data-driven PDE surrogates are trained with data produced by numerical PDE solvers.
arXiv:2509. 08765v4 Announce Type: replace-cross Abstract: Data-driven acceleration of scientific computing workflows has been a high-profile aim of machine learning (ML) for science, with numerical simulation of transient partial differential equations (PDEs) being one of the main applications.
arXiv:2509. 00203v3 Announce Type: replace Abstract: Parameterized partial differential equations (PDEs) underpin the mathematical modeling of complex systems in diverse domains, including engineering, healthcare, and physics.
arXiv:2606. 12182v1 Announce Type: new Abstract: Identifying the governing equations of complex dynamical systems remains a fundamental challenge across science and engineering.