Automated discovery of fundamental variables hidden in experimental data

All physical laws are described as mathematical relationships between state variables. These variables give a complete and non-redundant description of the relevant system. However, despite the prevalence of computing power and artificial intelligence, the process of identifying the hidden state variables themselves has resisted automation. Most data-driven methods for modelling physical phenomena still rely on the assumption that the relevant state variables are already known. A longstanding question is whether it is possible to identify state variables from only high-dimensional observational data. Here we propose a principle for determining how many state variables an observed system is likely to have, and what these variables might be. 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.