Reconstructing Attractors with Autoencoders

TL;DR

This paper demonstrates how to train autoencoders to reconstruct attractors from recorded data, effectively preserving the topology of the underlying phase space, with a focus on the Lorenz atmospheric convection system.

Contribution

It introduces a method for using autoencoders to reconstruct attractors while maintaining phase space topology, applied to a classic dynamical system.

Findings

Autoencoders can effectively reconstruct attractors from data.

The topology of the phase space is preserved in the reconstruction.

Demonstration on Lorenz system validates the approach.

Abstract

We show how to train an autoencoder to reconstruct an attractor from recorded footage, preserving the topology of the underlying phase space. This is explicitly demonstrated for the classic finite-amplitude Lorenz atmospheric convection problem.