arXiv Machine Learning August 3, 2026 By Quan Gu, Hongxia Liu

Feature Interaction Modeling for Physics-Informed Neural Networks and Neural Operators

Read the original on arXiv Machine Learning →

arXiv:2607. 28762v1 Announce Type: new Abstract: This work embeds feature interaction modules derived from factorization machines (FMs) into physics-informed neural networks (PINNs) and neural operator learning, to enhance model expressiveness for solution manifolds of parameterized partial differential equations (PDEs).

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

benchmarks

arXiv Machine Learning

Aug 11

Test-time Generalization for Physics through Neural Operator Splitting

arXiv:2602. 00884v2 Announce Type: replace Abstract: Neural operators have shown promise in learning solution maps of partial differential equations (PDEs), but they often struggle to generalize when test inputs lie outside the training distribution, such as novel initial conditions, unseen PDE coefficients or unseen physics.

By Louis Serrano, Jiequn Han, Edouard Oyallon, Shirley Ho, Rudy Morel

fine-tuning benchmarks

arXiv Machine Learning

Aug 11

Hierarchical rank-evolving representation for physics-informed neural networks

arXiv:2608. 09483v1 Announce Type: new Abstract: Recently, tensor-based physics-informed neural networks (T-PINNs) have received increasing attention.

By Ruoyang Su, Xi-Le Zhao, Kun Li, Liang Li

benchmarks

arXiv Machine Learning

23h ago

Estimating Parameter Fields in Multi-Physics PDEs from Scarce Measurements

arXiv:2509. 00203v3 Announce Type: replace Abstract: Parameterized partial differential equations (PDEs) underpin the mathematical modeling of complex systems in diverse domains, including engineering, healthcare, and physics.

By Xuyang Li, Mahdi Masmoudi, Rami Gharbi, Nizar Lajnef, Vishnu Naresh Boddeti

arXiv AI

Jun 3

Oscillatory State-Space Models as Inductive Biases for Physics-Informed Neural PDE Solvers

arXiv:2606. 02623v1 Announce Type: cross Abstract: Solving time-dependent partial differential equations (PDEs) is an important problem in computational science and engineering.

By Abhishek Chandra, Taniya Kapoor

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

5d ago

Physics-Informed Laplace Neural Operator for Solving Partial Differential Equations

arXiv:2602. 12706v2 Announce Type: replace Abstract: Neural operators have emerged as fast surrogate solvers for parametric partial differential equations (PDEs).

By Heechang Kim, Qianying Cao, Hyomin Shin, Seungchul Lee, George Em Karniadakis, Minseok Choi

rag diffusion benchmarks

Related stories

Test-time Generalization for Physics through Neural Operator Splitting

Hierarchical rank-evolving representation for physics-informed neural networks

Estimating Parameter Fields in Multi-Physics PDEs from Scarce Measurements

Oscillatory State-Space Models as Inductive Biases for Physics-Informed Neural PDE Solvers

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

Physics-Informed Laplace Neural Operator for Solving Partial Differential Equations