Learning Latent Dynamics for Partially-Observed Chaotic Systems

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.

References in corpus (9)

• Double-slit photoelectron interference in strong-field ionization of the neon dimer
• Discovering governing equations from data: Sparse identification of nonlinear dynamical systems
• On Dynamic Mode Decomposition: Theory and Applications
• Data-driven discovery of coordinates and governing equations
• Koopman invariant subspaces and finite linear representations of nonlinear dynamical systems for control
• Predicting catastrophes in nonlinear dynamical systems by compressive sensing
• Multistep Neural Networks for Data-driven Discovery of Nonlinear Dynamical Systems
• Deep reconstruction of strange attractors from time series
• EM-like Learning Chaotic Dynamics from Noisy and Partial Observations

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• Bounded nonlinear forecasts of partially observed geophysical systems with physics-constrained deep learning
• Early warning indicators via latent stochastic dynamical systems