variational methods

2 items

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.LG·5/8/2026

Data-Driven Variational Basis Learning Beyond Neural Networks: A Non-Neural Framework for Adaptive Basis Discovery

This manuscript introduces Data Driven Variational Basis Learning (DVBL), a novel non-neural framework for learning data-adaptive basis functions directly from high-dimensional data. It provides an explicit, interpretable, and mathematically transparent alternative to neural networks for representation learning, addressing their limitations in control and transparency.

variational methods Optimization machine learning data science