Discovering State Variables Hidden in Experimental Data

TL;DR

This paper introduces a novel method to identify the number and nature of hidden state variables in physical systems directly from video data, enabling better understanding and modeling without prior physics knowledge.

Contribution

The authors propose a new principle and algorithm to determine the intrinsic dimension and candidate state variables from high-dimensional observational data like videos.

Findings

Successfully identified state variables in various physical systems

Determined the intrinsic dimension of observed dynamics

Works without prior physics knowledge

Abstract

All physical laws are described as relationships between state variables that give a complete and non-redundant description of the relevant system dynamics. However, despite the prevalence of computing power and AI, the process of identifying the hidden state variables themselves has resisted automation. Most data-driven methods for modeling physical phenomena still assume that observed data streams already correspond to relevant state variables. A key challenge is to identify the possible sets of state variables from scratch, given only high-dimensional observational data. Here we propose a new principle for determining how many state variables an observed system is likely to have, and what these variables might be, directly from video streams. We demonstrate the effectiveness of this approach using video recordings of a variety of physical dynamical systems, ranging from elastic double pendulums to fire flames. Without any prior knowledge of the underlying physics, our algorithm discovers the intrinsic dimension of the observed dynamics and identifies candidate sets of state variables. We suggest that this approach could help catalyze the understanding, prediction and control of increasingly complex systems. Project website is at: https://www.cs.columbia.edu/~bchen/neural-state-variables