arXiv Machine Learning July 21, 2026 By Mikhail Khodak, Min Ki Jung, Brian Wynne, Edmond Chow, Egemen Kolemen

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

Read the original on arXiv Machine Learning →

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.

Summary generated by The Flow from the publisher's feed. The full article lives at arXiv Machine Learning.

reinforcement-learning

arXiv Machine Learning

Jul 24

FlashPDE: A Drop-In Fused Triton Operator Library for Neural PDE Solvers

arXiv:2607. 18020v2 Announce Type: replace Abstract: Physics-Informed Neural Networks (PINNs) solve PDEs by incorporating physical constraints into neural-network training, but large-scale problems are limited by automatic-differentiation memory overhead and inefficient execution of grid-based PDE operators.

By Peiyu Zang, Bosen Xie, Ruoxiang Xu, Yongqiang Cai

benchmarks

arXiv Machine Learning

Jul 21

FlashPDE: A Drop-in Fused Triton Operator Library for Neural PDE Solvers

arXiv:2607. 18020v1 Announce Type: new Abstract: Physics-Informed Neural Networks (PINNs) solve PDEs by incorporating physical constraints into neural-network training, but large-scale problems are limited by automatic-differentiation memory overhead and inefficient execution of grid-based PDE operators.

By Peiyu Zang, Bosen Xie, Ruoxiang Xu, Yongqiang Cai

benchmarks

arXiv Machine Learning

Jun 29

Mosaic: A Benchmark Suite for Differentiable Physics Solvers

arXiv:2606. 27895v1 Announce Type: cross Abstract: Differentiable partial differential equation (PDE) solvers underpin solver-in-the-loop ML training, gradient-based optimal control, and inverse problems, yet the practical cost of obtaining correct, usable gradients from a given solver on a given problem is largely undocumented.

By Andrin Rehmann, Heiko Zimmermann, Dion H\"afner

benchmarks

arXiv AI

Jul 14

Reinforcement Learning with Verifiable Physics: Post-training LLMs with Continuous Rewards

arXiv:2607. 10474v1 Announce Type: cross Abstract: Partial differential equations (PDEs) are foundational to modeling in science and engineering, but constructing reliable numerical solvers remains labor-intensive, demanding expert knowledge of discretization schemes, stability conditions, and boundary treatments.

By Pengfei Cai, Utkarsh Utkarsh, Alan Edelman, Christopher Vincent Rackauckas, Rafael Gomez-Bombarelli

llms reinforcement-learning benchmarks

arXiv Machine Learning

Jun 19

Learning universal approximations for partial differential equations with Physics-Informed Broad Learning System

arXiv:2606. 19754v1 Announce Type: new Abstract: Partial differential equations (PDEs) play a central role in modeling complex physical, biological, and engineering systems.

By Zhiwen Yu, Derong Yang, Liujian Zhang, Kaixiang Yang, Peilin Zhan, Jianmin Lv, Jane You, C. L. Philip Chen

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

Related stories

FlashPDE: A Drop-In Fused Triton Operator Library for Neural PDE Solvers

FlashPDE: A Drop-in Fused Triton Operator Library for Neural PDE Solvers

Mosaic: A Benchmark Suite for Differentiable Physics Solvers

Reinforcement Learning with Verifiable Physics: Post-training LLMs with Continuous Rewards

Learning universal approximations for partial differential equations with Physics-Informed Broad Learning System

Error-Conditioned Neural Solvers