partial differential equations

3 items

RESEARCHarXiv CS.LG·4/8/2026

A Theory-guided Weighted $L^2$ Loss for solving the BGK model via Physics-informed neural networks

Este artigo propõe uma função de perda L2 ponderada pela velocidade para resolver o modelo Bhatnagar-Gross-Krook (BGK) usando Redes Neurais Informadas pela Física (PINNs), superando as limitações da perda L2 padrão. A nova abordagem garante a convergência da solução aproximada e demonstra maior precisão e robustez em experimentos numéricos.

Physics-Informed Neural Networks Weighted L2 loss BGK model partial differential equations

RESEARCHarXiv CS.LG·4/20/2026

Python library supporting Discrete Variational Formulations and training solutions with Collocation-based Robust Variational Physics Informed Neural Networks (DVF-CRVPINN)

This paper explores solving Partial Differential Equations (PDEs) using discrete weak formulations and a discrete neural network representation. It proposes a Python environment and a DVF-CRVPINN approach for training solutions, applying discrete automatic differentiation for equations like 2D Stokes.

variational methods Numerical Methods Physics-Informed Neural Networks partial differential equations

RESEARCHarXiv CS.AI·5/1/2026

Compositional Meta-Learning for Mitigating Task Heterogeneity in Physics-Informed Neural Networks

This paper proposes LAM-PINN, a compositional meta-learning framework designed to mitigate task heterogeneity in Physics-Informed Neural Networks (PINNs). It addresses the challenge of training PINNs for families of partial differential equations (PDEs) which often face high computational costs or negative transfer under data-scarce conditions.

Meta-Learning neural networks Physics-Informed Neural Networks partial differential equations