Work

DeepPropNet - A recursive deep neural network propagator for learning evolutionary PDE operators

Year: 2025

Type: article

Abstract: In this paper, we propose a deep neural network approximation to the evolution operator for time-dependent PDE systems over long time period by recursively using one single neural network propagator, in the form of POD-DeepONet with built-in causality feature, for a small time interval.The trained DeepPropNet of moderate size is shown to give accurate prediction of wave solutions over the whole time interval.

Source: Beijing Journal of Pure and Applied Mathematics

DOI: 10.4310/bpam.250414235900

Authors: Lizuo Liu, Wei Cai

Institution: Southern Methodist University

Language: English

Topic: Model Reduction and Neural Networks

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: bronze

Funder: National Science Foundation

Award: Deep Neural Network Machine Learning for Oscillatory Navier-Stokes Flows and Nonlinear Operators, and High Dimensional Fokker-Planck Equations