Learning Iterated Function Systems from Time Series of Partial Observations

TL;DR

This paper introduces a method to learn the structure of complex dynamical systems from partial time-series data using delay embeddings, resulting in a minimal, diffeomorphic model representation.

Contribution

It presents a novel approach to reconstruct finitely generated random iterated function systems from partial observations with delay embeddings.

Findings

Successfully reconstructs the original system dynamics

Provides a minimal, diffeomorphic model representation

Applicable to systems with partial and noisy data

Abstract

We develop a methodology to learn finitely generated random iterated function systems from time-series of partial observations using delay embeddings. We obtain a minimal model representation for the observed dynamics, using a hidden variable representation, that is diffeomorphic to the original system.