arXiv Machine Learning July 14, 2026 By Zhangyi Lian, Xinda Dong, Wenxuan Huo, Weifeng Huang, Gang Zhu, Qiang He

Multi-dimensional training-priority weighting based on physical information propagation paths: a unified residual-weighting framework for physics-informed neural networks

Read the original on arXiv Machine Learning →

arXiv:2607. 11094v1 Announce Type: new Abstract: Physics-informed neural networks (PINNs) have shown promise for solving partial differential equations (PDEs); however, their synchronous optimization treats residuals of different regions and constraints equally, which is inconsistent with the progressive "from source to response" physical information propagation path, degrading training stability and accuracy.

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benchmarks

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

Jun 5

Effective Dimensionality as an Operator Invariant for Physics-Preserving Constraint Adaptation in Physics-Informed Neural Networks

arXiv:2606. 06171v1 Announce Type: cross Abstract: Physics-Informed Neural Networks inherently suffer from task interference because they rely on a shared parameter space to satisfy both governing differential equations and boundary conditions.

By Cornelius Otchere, Michael Shields

fine-tuning

arXiv Machine Learning

Sep 15

Architecture--Optimization Co-Design for Physics-Informed Neural Networks via Layer-wise Coordinate Adaptation and Gradient Conflict Resolution

arXiv:2601.12971v2 Announce Type: replace Abstract: Physics-informed neural networks (PINNs) can be limited by coordinate representations and conflicting gradients from heterogeneous physical constra...

By Pancheng Niu, Jun Guo, Qiaolin He, Yongming Chen, Yanchao Shi

benchmarks

arXiv Machine Learning

Jun 5

On the training of physics-informed neural operators for solving parametric partial differential equations

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By Nanxi Chen, Chuanjie Cui, Airong Chen, Sifan Wang, Rujin Ma

llms computer-vision benchmarks

arXiv Machine Learning

Jun 4

Loss-Conditional PINNs for Parametric PDE Families

arXiv:2606. 04420v1 Announce Type: new Abstract: Physics-informed neural networks (PINNs) approximate solutions of ODEs and PDEs by minimising a weighted combination of residual, boundary, initial, and data losses.

By Anna Lazareva, Alexander Tarakanov

arXiv Machine Learning

5d ago

Gradient Surgery for Physics-Informed Neural Networks

The paper introduces PAM-GS, a physics-aware gradient surgery technique for Physics-Informed Neural Networks (PINNs). It addresses the highly imbalanced multi-task optimisation problem in PINNs by adaptively mitigating task interference based on observed gradient conflicts. Experiments on four PDE benchmarks show that PAM-GS achieves competitive solution accuracy while maintaining strong task-balanced performance, outperforming existing methods on most problems.

By Thomas Borsani, Giuseppe Di Fatta

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