Exploring Nonlinear System with Machine Learning: Chua and Lorenz Circuits Analyzed

TL;DR

This paper applies an upgraded neural network-based symbolic regression model to analyze and recognize the differential equations of Chua's and Lorenz circuits, demonstrating robustness and providing insights into nonlinear circuit dynamics.

Contribution

It introduces an improved SINDy-PI model for systematically analyzing nonlinear circuits with machine learning, including noise resistance and data precision effects.

Findings

The model accurately recognizes differential equations within certain data ranges.

Lorenz circuit exhibits better noise resistance than Chua's circuit.

The approach offers a foundation for studying nonlinear systems with deep learning.

Abstract

Nonlinear circuits serve as crucial carriers and physical models for investigating nonlinear dynamics and chaotic behavior, particularly in the simulation of biological neurons. In this study, Chua's circuit and Lorenz circuit are systematically explored for the first time through machine learning correlation algorithms. Specifically, the upgraded and optimized SINDy-PI model, which is based on neural network and symbolic regression algorithm, is utilized to learn the numerical results of attractors generated by these two nonlinear circuits. Through error analysis, we examine the effects of the precision of input data and the amount of data on the algorithmic model. The findings reveal that when the input data quantity and data precision fall within a certain range, the algorithm model can effectively recognize and restore the differential equation expressions corresponding to the two circuits. Additionally, we test the anti-interference ability of different circuits and the robustness of the algorithm by introducing noise into the test data. The results indicate that under the same noise disturbance, the Lorenz circuit has better noise resistance than Chua's circuit, providing a starting point for further studying the intrinsic properties and characteristics of different nonlinear circuits. The above results will not only offer a reference for the further study of nonlinear circuits and related systems using deep learning algorithms but also lay a preliminary theoretical foundation for the study of related physical problems and applications.