# Learning Latent Dynamics for Partially-Observed Chaotic Systems

## TL;DR

This paper introduces a neural network-based framework for identifying latent dynamical models of partially-observed chaotic systems, improving forecasting accuracy and long-term behavior prediction over existing methods.

## Contribution

It presents a novel approach that jointly learns an ODE in latent space and reconstructs states, integrating ideas from Koopman theory and Takens' theorem.

## Key findings

- Outperforms state-of-the-art methods in short-term forecasting
- Accurately captures long-term asymptotic patterns
- Provides a unified neural network framework for latent dynamics

## Abstract

This paper addresses the data-driven identification of latent dynamical representations of partially-observed systems, i.e., dynamical systems for which some components are never observed, with an emphasis on forecasting applications, including long-term asymptotic patterns. Whereas state-of-the-art data-driven approaches rely on delay embeddings and linear decompositions of the underlying operators, we introduce a framework based on the data-driven identification of an augmented state-space model using a neural-network-based representation. For a given training dataset, it amounts to jointly learn an ODE (Ordinary Differential Equation) representation in the latent space and reconstructing latent states. Through numerical experiments, we demonstrate the relevance of the proposed framework w.r.t. state-of-the-art approaches in terms of short-term forecasting performance and long-term behaviour. We further discuss how the proposed framework relates to Koopman operator theory and Takens' embedding theorem.