arXiv Machine Learning By Sahana Rayan, Yash Patel, Ambuj Tewari

A Greedy PDE Router for Blending Neural Operators and Classical Methods

Read the original on arXiv Machine Learning →

A Greedy PDE Router for Blending Neural Operators and Classical Methods proposes an approximate greedy router that selects solvers from an ensemble to solve PDEs efficiently. The method addresses the challenge of lacking true error knowledge by mimicking greedy selection, aiming to combine the strengths of machine learning and classical solvers. Experiments on Poisson, convection-diffusion, and anisotropic diffusion equations demonstrate reduced time-to-solution compared to single-solver baselines and existing hybrid approaches such as HINTS.

Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv Machine Learning.

arXiv AI
Jun 26

Error-Conditioned Neural Solvers

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.

By Haina Jiang, Liam Wang, Peng-Chen Chen, Min Seop Kwak, Seungryong Kim, Brian Bell, Jeong Joon Park
arXiv Machine Learning
Jul 21

One-shot acceleration of transient PDE solvers via online-learned preconditioners

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.

By Mikhail Khodak, Min Ki Jung, Brian Wynne, Edmond Chow, Egemen Kolemen
arXiv AI
Jun 3

Physics-informed diffusion models in spectral space

arXiv:2602. 09708v2 Announce Type: replace-cross Abstract: We propose physics-informed spectral diffusion (PISD), a methodology that combines generative latent diffusion models with physics-informed machine learning to generate solutions of partial differential equations (PDEs) conditioned on partial observations, which includes, in particular, forward and inverse PDE problems.

By Davide Gallon, Philippe von Wurstemberger, Patrick Cheridito, Arnulf Jentzen