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.