Learning Physics from Movies: Discovering Dynamical State Variables

Understanding the dynamics of physical systems requires identifying dynamical state variables and describing their temporal evolution. While feasible for low-dimensional systems with known variables, this becomes intractable for high-dimensional systems when the variables are unknown and only observations are available. For example, in a video of a moving object, many of the thousands of pixels are redundant and can be compressed to a few dynamical state variables. We find these low-dimensional variables using an adaptation of the Deep Variational Symmetric Information Bottleneck (DVSIB) applied to time series. DVSIB compresses two variables while maximizing the mutual information between their compressed representations. We split the data into past and future segments and use DVSIB to discover the minimal state variables needed to describe the system's evolution. Even when the number of observations is of order of the original data's dimensionality, DVSIB identifies the system's state variables, determines their dimensionality, and retrieves the geometric and topological structure of the phase space. We demonstrate this on multiple physical systems, showing its ability to extract meaningful low-dimensional representations from complex, high-throughput data.