An Improved Autoencoder Conjugacy Network to Learn Chaotic Maps

TL;DR

This paper presents an enhanced autoencoder network with a conjugacy layer that effectively learns chaotic maps by transforming complex dynamics into simpler forms, improving accuracy and stability.

Contribution

It introduces a novel autoencoder architecture with a conjugacy layer that enforces dynamical principles, advancing the learning of chaotic maps.

Findings

Successfully learns continuous and piecewise chaotic maps

Outperforms traditional and recent deep learning methods

Demonstrates improved accuracy and stability

Abstract

We introduce a method for learning chaotic maps using an improved autoencoder neural network that incorporates a conjugacy layer in the latent space. The added conjugacy layer transforms nonlinear maps into a simple piecewise linear map (the tent map) whilst enforcing dynamical principles of well-known and defective conjugacy functions that increase the accuracy and stability of the learned solution. We demonstrate the method's effectiveness on both continuous and piecewise chaotic one-dimensional maps and numerically illustrate improved performance over related traditional and recently emerged deep learning architectures.