Variational Integrator Networks for Physically Structured Embeddings

TL;DR

This paper introduces variational integrator networks, a novel neural network architecture that preserves the geometric structure of physical systems, enabling accurate, interpretable, and data-efficient modeling of dynamical systems from various data sources.

Contribution

It presents a new class of neural networks that incorporate geometric structure preservation, improving long-term prediction and interpretability in dynamical system modeling.

Findings

Accurately learns dynamical systems from noisy phase space data

Effective in modeling dynamics from image pixels

Enhances long-term prediction stability

Abstract

Learning workable representations of dynamical systems is becoming an increasingly important problem in a number of application areas. By leveraging recent work connecting deep neural networks to systems of differential equations, we propose \emph{variational integrator networks}, a class of neural network architectures designed to preserve the geometric structure of physical systems. This class of network architectures facilitates accurate long-term prediction, interpretability, and data-efficient learning, while still remaining highly flexible and capable of modeling complex behavior. We demonstrate that they can accurately learn dynamical systems from both noisy observations in phase space and from image pixels within which the unknown dynamics are embedded.