arXiv Machine Learning By Quan Gu, Hongxia Liu

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

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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).

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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
arXiv Machine Learning
Aug 19

Estimating Parameter Fields in Multi-Physics PDEs from Scarce Measurements

The paper introduces Neptune, a method that uses independent coordinate neural networks to infer parameter fields in multi-physics PDEs from sparse measurements. Neptune can accurately estimate parameters with nonlinear, spatiotemporal variations, outperforming existing techniques by reducing estimation errors by up to two orders of magnitude and improving dynamic response predictions by a factor of ten. It also demonstrates strong physical extrapolation, enabling reliable predictions beyond the training data.

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