arXiv Machine Learning June 29, 2026 By Andrin Rehmann, Heiko Zimmermann, Dion H\"afner

Mosaic: A Benchmark Suite for Differentiable Physics Solvers

Read the original on arXiv Machine Learning →

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.

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

benchmarks

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

reinforcement-learning

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 Machine Learning

Jul 27

Energy Manifold Natural Gradient Descent: Riemannian Optimization for Neural PDE Solvers

arXiv:2607. 22004v1 Announce Type: new Abstract: Energy natural gradient descent (ENGD) aligns parameter updates with the curvature of an underlying function-space energy, but existing formulations assume an unconstrained Euclidean parameter domain.

By Zhangyong Liang, Huanhuan Gao

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 11

Adjoint Method versus Physics-Informed Neural Networks in PDE-Constrained Inverse Problems

arXiv:2606. 12337v1 Announce Type: cross Abstract: Inverse problems governed by partial differential equations (PDEs) are central to computational mechanics and are commonly solved by adjoint-based optimization, while physics-informed neural networks (PINNs) have emerged as a flexible alternative.

By Zhen Zhang, Alessandro Alla, George Em Karniadakis

benchmarks

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

Related stories

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

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

Energy Manifold Natural Gradient Descent: Riemannian Optimization for Neural PDE Solvers

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

Adjoint Method versus Physics-Informed Neural Networks in PDE-Constrained Inverse Problems

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