Learning Latent Dynamics for Partially-Observed Chaotic Systems

Said ouala, Duong Nguyen, Lucas Drumetz, Bertrand Chapron, Ananda Pascual, Fabrice Collard, Lucile Gaultier, Ronan Fablet

TL;DR: Data driven identification of ODE representations for partially observed chaotic systems

Abstract: This paper addresses the data-driven identification of latent representations of partially-observed dynamical systems, i.e. dynamical systems whose some components are never observed, with an emphasis on forecasting applications and 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 reconstructing the latent states and learning an ODE (Ordinary Differential Equation) representation in this space. 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 errors and long-term behaviour. We further discuss how the proposed framework relates to Koopman operator theory and Takens' embedding theorem.

Keywords: Dynamical systems, Neural networks, Embedding, Partially observed systems, Forecasting, chaos

Community Implementations: [ 1 code implementation](https://www.catalyzex.com/paper/arxiv:1907.02452/code)