用随机测试函数差分解偏微分方程，免求导更稳定。

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

• 将随机差分算子作用于测试函数，构建无导数的弱对抗框架
• 适用于福克-普朗克型二阶椭圆与抛物方程，无需计算解网络梯度
• 适合追求高稳定性与低复杂度的PDE求解场景

我们提出ARDO方法，用于通过深度学习技术求解偏微分方程及相关的难题。该方法采用弱对抗形式，但将随机差分算子转移到测试函数上。其主要优势在于对解神经网络完全无导数依赖。该框架特别适用于福克-普朗克型二阶椭圆与抛物型偏微分方程。

原文摘要 · Abstract (English)

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.

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