Learning Dynamical Systems from Noisy Sensor Measurements using Multiple Shooting
This addresses the challenge of instability in learning dynamical systems from data, which is crucial for applications in physics and engineering, representing a novel method for a known bottleneck.
The paper tackles the problem of learning dynamical systems from noisy sensor measurements by introducing a multiple shooting-based method, achieving state-of-the-art performance on systems observed from raw images and demonstrating robustness to noise and complexity.
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.