Learning Dynamical Systems from Noisy Sensor Measurements using Multiple Shooting

TL;DR

This paper introduces a scalable multiple shooting method for learning latent dynamical system representations from noisy sensor data, achieving state-of-the-art results especially on image-based and chaotic systems.

Contribution

The paper presents a novel multiple shooting approach that improves robustness and scalability in learning dynamical systems from noisy measurements, including complex and chaotic systems.

Findings

State-of-the-art performance on image-based systems

Robustness to noisy sensor data

Effective on complex chaotic systems

Abstract

Modeling dynamical systems plays a crucial role in capturing and understanding complex physical phenomena. When physical models are not sufficiently accurate or hardly describable by analytical formulas, one can use generic function approximators such as neural networks to capture the system dynamics directly from sensor measurements. As for now, current methods to learn the parameters of these neural networks are highly sensitive to the inherent instability of most dynamical systems of interest, which in turn prevents the study of very long sequences. In this work, we introduce a generic and scalable method based on multiple shooting to learn latent representations of indirectly observed dynamical systems. We achieve state-of-the-art performances on systems observed directly from raw images. Further, we demonstrate that our method is robust to noisy measurements and can handle complex dynamical systems, such as chaotic ones.