Discovering State Variables Hidden in Experimental Data
This addresses the challenge of automating state variable discovery for complex systems, potentially aiding in understanding, prediction, and control, though it appears incremental as it builds on existing data-driven methods.
The authors tackled the problem of automatically identifying hidden state variables from high-dimensional observational data, such as video streams, without prior knowledge of the underlying physics. They demonstrated their algorithm on systems like elastic double pendulums and fire flames, discovering the intrinsic dimension and candidate state variables.
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