Local Polynomial Regression for Learning Dynamical Systems

Thomas M. Menino Convention & Exhibition Center 

We propose a local polynomial regression framework for discovering governing equations of dynamical systems from noisy time-indexed data. The method estimates both the latent state and its time derivative under Gaussian measurement error, illustrated using an exponential growth model. Closed-form local estimators enable recovery of the underlying dynamics without global parametric assumptions. The approach is extended to incorporate random effects, allowing for subject-specific heterogeneity in growth dynamics. Simulation studies demonstrate accurate recovery of the governing equations under moderate noise, highlighting the method's flexibility for longitudinal and repeated-measures data.

Dynamical systems

Local Polynomial Regression