ARDO: A Weak Formulation Deep Neural Network Method for Elliptic and Parabolic PDEs Based on Random Differences of Test Functions
This method addresses PDE-solving problems in computational physics and engineering, but it appears incremental as it builds on existing weak adversarial formulations with a specific modification.
The authors tackled solving elliptic and parabolic PDEs by proposing the ARDO method, a derivative-free deep learning approach based on a weak adversarial formulation with random differences of test functions, achieving a framework suitable for Fokker-Planck type equations.
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.