Discovering interpretable low-dimensional dynamics using maximum entropy

Models (i.e., governing equations) are fundamental to science and engineering. Advances in data acquisition now make it possible to extract interpretable, low-dimensional descriptions from high-dimensional observations. However, existing approaches sacrifice either interpretability for reconstruction accuracy or infer symbolic dynamics without relating latent coordinates to physically meaningful observables. Here we present Edwin (maximum entropy-driven compression with interpretable nonlinear model discovery), a unified framework that simultaneously performs dimensionality reduction using the dynamic maximum entropy (DME) principle and discovers sparse symbolic models governing latent dynamics, as well as the coupling between learned features and external metadata. We validate Edwin on diverse simulated systems, including stochastic diffusion, the Ornstein-Uhlenbeck process, self-assembling particles, and neural population firing rates, as well as on a noisy experimental time series of aggregating RNA-liposome complexes. Across all systems, Edwin recovers low-dimensional symbolic models that are physically interpretable and generalize to unseen conditions. Together, these results establish Edwin as a principled framework for inferring interpretable, low-dimensional dynamics from high-dimensional nonnegative data.