An Improved Autoencoder Conjugacy Network to Learn Chaotic Maps

2025/07/14 by Meagan Carney, Cecilia González‐Tokman, Carney, Meagan +5
Computer Science · #Dynamical Systems (math.DS) #FOS: Mathematics #Image Processing and 3D Reconstruction #Neural Networks and Applications

paper · pdf · doi:10.48550/arxiv.2507.09835

openalex publication_date 2025/07/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Differentiable conjugacies for one-dimensional maps
• Controlling nonlinear dynamical systems into arbitrary states using\n machine learning
• Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
• Model reduction of dynamical systems on nonlinear manifolds using deep\n convolutional autoencoders
• Model reduction of dynamical systems on nonlinear manifolds using deep convolutional autoencoders
• Linearly-Recurrent Autoencoder Networks for Learning Dynamics
• Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles
• Extremes and Recurrence in Dynamical Systems
• Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning

Related

• Deep Learning of Chaos Classification
• Exploiting Chaotic Dynamics as Deep Neural Networks
• Deep Learning for Prediction and Classifying the Dynamical behaviour of Piecewise Smooth Maps
• Deep Learning of Chaotic Systems from Partially-Observed Data
• Inferring stability properties of chaotic systems on autoencoders' latent spaces