Deep-learning of parametric partial differential equations from sparse and noisy data

• DOI: 10.1063/5.0042868
• Publication Date: 2021-03-26T10:55:47Z
• Authors: Hao Xu; Dongxiao Zhang; Junsheng Zeng
• Keywords: FOS: Computer and information sciences; Computer Science - Machine Learning; Computer Science - Artificial Intelligence; Computer Science - Neural and Evolutionary Computing; FOS: Physical sciences; Machine Learning (stat.ML); Computational Physics (physics.comp-ph); 01 natural sciences; Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Statistics - Machine Learning; 0103 physical sciences; Neural and Evolutionary Computing (cs.NE); Physics - Computational Physics

Data-driven methods have recently made great progress in the discovery of partial differential equations (PDEs) from spatial-temporal data. However, several challenges remain to be solved, including sparse noisy data, incomplete candidate library, and spatially- or temporally-varying coefficients. In this work, a new framework, which combines neural network, genetic algorithm adaptive methods, is put forward address all these simultaneously. trained network utilized calculate derivatives generate large amount meta-data, solves problem Next, discover form PDEs corresponding coefficients with an library. Finally, two-step method introduced parametric method, structure PDE first discovered, then general varying identified. The proposed tested on Burgers equation, convection-diffusion wave KdV equation. results demonstrate that robust able