Discovering sparse interpretable dynamics from partial observations

Identifying the governing equations of a nonlinear dynamical system enables physical understanding and accurate, generalizable modeling, but is challenging with partial observations. The authors propose a machine learning framework that discovers governing equations using only partial measurements by combining a learned encoder for hidden-state reconstruction with a sparse symbolic model for dynamics. The architecture is trained end-to-end by matching higher-order symbolic time derivatives of the model (via automatic differentiation) to finite-difference estimates from data. Across multiple ODE and PDE benchmarks, the method reconstructs full system states and identifies equations of motion from partial observations.

Peter Y. Lu, Joan Ariño Bernad, Marin Soljačić