arXiv Machine Learning

Tackling Failure Modes of PINNs and PIKANs Using Conflict-Free Gradients

arXiv AI

Jul 17

LIGO-PINN: Learned Initialization via Gated Optimization to Alleviate Convergence Failures in Physics Informed Neural Networks

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).

By Nilay Anurag, Shital Adhikari, Taniya Kapoor, Nikhil Muralidhar

benchmarks

arXiv Machine Learning

Aug 10

Mitigating Gradient Pathology in PINNs through Aligned Constraint

arXiv:2605. 25001v2 Announce Type: replace Abstract: While Physics-Informed Neural Networks (PINNs) are powerful for solving Partial Differential Equations (PDEs), their training is often paralyzed by gradient pathology.

By Yichen Luo, Peiyu Zhu, Dongxiao Hu, Jia Wang, Tailin Wu, Dapeng Lan, Yu Liu, Zhibo Pang

arXiv Machine Learning

Sep 10

Latent-MoE: Domain-Aware Mixture-of-Experts for PDEs with Multi-Regime Physics

arXiv:2609.07814v1 Announce Type: new Abstract: Physics-informed neural networks (PINNs) struggle on PDEs whose governing physics varies across the domain. We trace this to a structural property of s...

By Hanwen Wang, Paris Perdikaris

benchmarks

arXiv Machine Learning

Jul 27

Latent PDE mapping for efficient physics-informed learning across geometries with limited data

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.

By Ingvild Askim Adde, Mary M. Maleckar, Gabriel Balaban

benchmarks

arXiv AI

Jun 10

Structure-Preserving Learning Improves Geometry Generalization in Neural PDEs

arXiv:2602. 02788v2 Announce Type: replace-cross Abstract: We aim to develop physics foundation models for science and engineering that provide real-time solutions to Partial Differential Equations (PDEs) which preserve structure and accuracy under adaptation to unseen geometries.

By Benjamin D. Shaffer, Shawn Koohy, Brooks Kinch, M. Ani Hsieh, Nathaniel Trask

llms benchmarks safety

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

Aug 26

Do physics-informed neural networks (PINNs) need to be deep? Shallow PINNs using the Levenberg-Marquardt algorithm

arXiv:2602.08515v3 Announce Type: replace-cross Abstract: This work investigates shallow physics-informed neural networks (PINNs) for solving forward and inverse problems governed by nonlinear partia...

By Muhammad Luthfi Shahab, Imam Mukhlash, Hadi Susanto

arXiv Machine Learning

Jul 10

PGD-NO: A Neural Operator with Precomputed Geometry Decomposition for 3D Million-scale Physics Simulations

arXiv:2607. 08025v1 Announce Type: new Abstract: While neural PDE solvers have demonstrated significant potential for accelerating engineering simulations, existing architectures remain constrained by high memory consumption and the single node bottleneck, where the maximum processable mesh resolution is strictly limited by the VRAM of a single compute unit.

By Weiheng Zhong, Jing Bi, Victor Oancea, Hadi Meidani

benchmarks safety

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

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

Aug 11

ProPINN: Demystifying Propagation Failures in Physics-Informed Neural Networks

arXiv:2502. 00803v3 Announce Type: replace Abstract: Physics-informed neural networks (PINNs) have earned high expectations in solving partial differential equations (PDEs), but their optimization usually faces thorny challenges due to the unique derivative-dependent loss function.

By Yuezhou Ma, Haixu Wu, Hang Zhou, Huikun Weng, Jianmin Wang, Mingsheng Long

llms

arXiv Machine Learning

Jul 2

GAIA: Geometry-Adaptive Operator Learning for Forward and Inverse Problems

arXiv:2607. 01128v1 Announce Type: new Abstract: Operator learning for partial differential equations (PDEs) on arbitrary geometries builds fast neural surrogates for large-scale simulation.

By Meenakshi Krishnan, Pranav Pulijala, Ke Chen, Haizhao Yang, Ramani Duraiswami

llms benchmarks

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