Application of Lie Group-based Neural Network Method to Nonlinear Dynamical Systems

TL;DR

This paper introduces a Lie group-based neural network approach for solving nonlinear dynamical systems' initial value problems, emphasizing its efficiency and high performance demonstrated through various examples.

Contribution

It presents a novel, computationally efficient neural network method based on Lie groups for nonlinear dynamics, outperforming multilayer perceptrons.

Findings

The method is significantly cheaper than multilayer perceptrons.

It demonstrates higher performance in solving nonlinear dynamical systems.

Several examples validate the effectiveness of the approach.

Abstract

In this paper, a Lie group-based neural network method is proposed for solving initial value problems of non linear dynamics. Due to its single-layer structure (MLP), the approach is substantially cheaper than the multilayer perceptron method used in literature. The higher performance ability of the method is demonstrated by several examples.