Extracting Interpretable Physical Parameters from Spatiotemporal Systems using Unsupervised Learning*

Real-world data from spatiotemporal systems is often difficult to analyze and interpret due to complex dynamics as well as uncontrolled experimental variables. We demonstrate an unsupervised machine learning technique for extracting interpretable physical parameters from noisy spatiotemporal data and for building a transferable predictive model of the system. This is accomplished without prior knowledge of the underlying dynamics or the governing partial differential equation (PDE). Numerical experiments using simulated data governed by PDEs show that our method accurately identifies and extracts relevant parameters that characterize independent variations in the system dynamics. Our method for discovering interpretable latent parameters in spatiotemporal systems will allow us to better understand real-world phenomena by analyzing datasets with varying dynamical behaviors that are difficult to disentangle.