# Discovering State Variables Hidden in Experimental Data

arXiv: https://arxiv.org/abs/2112.10755 · HTML: https://mlsanity.com/paper/2112.10755/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 0 of its 7 references that are in the map.
- First posted on arXiv 20 Dec 2021.

## Built on by (most cited first, 12 of 12)

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- [LyTimeT: Towards Robust and Interpretable State-Variable Discovery](https://mlsanity.com/paper/2510.19716/) (2025)
- [A Relational Macrostate Theory Guides Artificial Intelligence to Learn Macro and Design Micro](https://mlsanity.com/paper/2210.07374/) (2022)
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- [Discovering Car-following Dynamics from Trajectory Data through Deep Learning](https://mlsanity.com/paper/2408.00251/) (2024)
- [How AI Agents Discover Scientific Equations: From Hydrotope Rediscovery to New Water-Wave Amplitudes](https://mlsanity.com/paper/2610.00435/) (2026)

## Abstract (arXiv)

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