Discovering interpretable low-dimensional dynamics using maximum entropy

TL;DR

Edwin is a unified framework that combines maximum entropy principles with symbolic model discovery to extract interpretable, low-dimensional dynamics from high-dimensional data across various systems.

Contribution

It introduces a novel approach that simultaneously reduces dimensionality and discovers sparse, interpretable models linking latent features to physical observables.

Findings

Successfully recovers low-dimensional symbolic models across diverse systems.

Generalizes well to unseen conditions in both simulated and experimental data.

Provides physically interpretable models that connect latent dynamics to external metadata.

Abstract

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, spiking neural populations, and low rank recurrent neural networks, 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 powerful framework for inferring interpretable, low dimensional dynamics directly from high dimensional data.