Work

Training data studies for the cell-average-based neural network method for linear hyperbolic and parabolic equations

Year: 2025

Type: article

Abstract: In this paper, we conduct training data studies for the cell-averagebased neural network (CANN) method for linear hyperbolic and parabolic equations.We enlarge the training data set to include representative solution trajectories such as Fourier basis functions and determine whether the method will be improved.A perturbed stochastic gradient descent method is proposed and is verified to improve the method's stability after long-time simulations.The robustness of the method to contaminated training data is investigated.For the linear parabolic equation, the CANN method can be generalized to solve a large group of initial value problems, especially those involving high-frequency modes, while being an explicit method with a large time step size applied to evolve the solution forward in time.MSC 2020 subject classifications: 65M25.

Source: Beijing Journal of Pure and Applied Mathematics

DOI: 10.4310/bpam.250414232842

Authors: Tyler Kroells, Ethan Schmidt, Changxin Qiu, Jue Yan

Institutions: Iowa State University, Ningbo 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

Funders: National Science Foundation, National Natural Science Foundation of China, Natural Science Foundation of Ningbo

Awards: G1315230015, Positivity preserving limiter and new development on elliptic interface problems, G5418499669