ARDO: A Weak Formulation Deep Neural Network Method for Elliptic and Parabolic PDEs Based on Random Differences of Test Functions
Numerical Analysis
2025-09-05 v1 Artificial Intelligence
Numerical Analysis
Abstract
We propose ARDO method for solving PDEs and PDE-related problems with deep learning techniques. This method uses a weak adversarial formulation but transfers the random difference operator onto the test function. The main advantage of this framework is that it is fully derivative-free with respect to the solution neural network. This framework is particularly suitable for Fokker-Planck type second-order elliptic and parabolic PDEs.
Cite
@article{arxiv.2509.03757,
title = {ARDO: A Weak Formulation Deep Neural Network Method for Elliptic and Parabolic PDEs Based on Random Differences of Test Functions},
author = {Wei Cai and Andrew Qing He},
journal= {arXiv preprint arXiv:2509.03757},
year = {2025}
}