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arXiv · 2507.09835

An Improved Autoencoder Conjugacy Network to Learn Chaotic Maps

Meagan Carney·Cecilia González-Tokman·Ruethaichanok Kardkasem·Hongkun Zhang
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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.

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Meagan Carney, Cecilia González-Tokman, Ruethaichanok Kardkasem, Hongkun Zhang. 2025-07-14. An Improved Autoencoder Conjugacy Network to Learn Chaotic Maps. https://arxiv.org/abs/2507.09835

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