ARDO: A Weak Formulation Deep Neural Network Method for Elliptic and Parabolic PDEs Based on Random Differences of Test Functions

Wei Cai, Andrew Qing He
9/3/2025
math.NAcs.AI

No confident code implementation found for this paper.

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.

View on arXivView PDF

Code Implementations

No confident code match yet

We couldn't find an author-owned or strongly-evidenced community implementation for this paper. Any repos shown below are weak matches — verify before relying on them.

No code implementations found yet.

Know of an implementation? Let us know in the comments below!

Similar Papers

Error Analysis of Three-Layer Neural Network Trained with PGD for Deep Ritz Method

81% match2024

Convergence Analysis of the Deep Galerkin Method for Weak Solutions

80% match2023

A Variational Physics-Informed Neural Network Framework Using Petrov-Galerkin Method for Solving Singularly Perturbed Boundary Value Problems

80% match2025

Learning Discontinuous Galerkin Solutions to Elliptic Problems via Small Linear Convolutional Neural Networks

80% match2025

Building Trust in PINNs: Error Estimation through Finite Difference Methods

79% match2026

First Order System Least Squares Neural Networks

79% match2024

Cite this paper

@article{cai2025ardo,
  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},
  year   = {2025},
  eprint = {2509.03757},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2509.03757v1}
}

Add a badge to your README

Shows whether official code is linked for this paper.

Code of Paper badge
[![Code of Paper](https://codeofpaper.com/badge/2509.03757.svg)](https://codeofpaper.com/paper/2509.03757)

Discussion