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In this paper, we address the challenge of deriving dynamical models fromsparse and noisy data. High-quality data is crucial for symbolic regressionalgorithms; limited and noisy data can present modeling challenges. To overcomethis, we combine Gaussian process regression with a sparse identification ofnonlinear dynamics (SINDy) method to denoise the data and identify nonlineardynamical equations. Our approach GPSINDy offers improved robustness withsparse, noisy data compared to SINDy alone. We demonstrate its effectiveness onsimulation data from Lotka-Volterra and unicycle models and hardware data froman NVIDIA JetRacer system. We show superior performance over baselinesincluding more than 50% improvement over SINDy and other baselines inpredicting future trajectories from noise-corrupted and sparse 5 Hz data.

Symbolic Regression on Sparse and Noisy Data with Gaussian Processes