Learning Dynamical Systems from Noisy Sensor Measurements using Multiple Shooting

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.

References in corpus (13)

• PyTorch: An Imperative Style, High-Performance Deep Learning Library
• Unsupervised Learning of Video Representations using LSTMs
• On the Properties of Neural Machine Translation: Encoder-Decoder Approaches
• Chaos as an Intermittently Forced Linear System
• Deep multi-scale video prediction beyond mean square error
• Stochastic Adversarial Video Prediction
• Deep learning of dynamics and signal-noise decomposition with time-stepping constraints
• Deep Reinforcement Learning in a Handful of Trials using Probabilistic Dynamics Models
• Deep Kalman Filters
• Deep Variational Bayes Filters: Unsupervised Learning of State Space Models from Raw Data
• On the smoothness of nonlinear system identification
• Recurrent Kalman Networks: Factorized Inference in High-Dimensional Deep Feature Spaces
• Nonlinear Evolution via Spatially-Dependent Linear Dynamics for Electrophysiology and Calcium Data