Title: Symbolic Regression on Sparse and Noisy Data with Gaussian Processes

Abstract: In this paper, we address the challenge of deriving dynamical models from sparse and noisy data. High-quality data is crucial for symbolic regression algorithms; limited and noisy data can present modeling challenges. To overcome this, we combine Gaussian process regression with a sparse identification of nonlinear dynamics (SINDy) method to denoise the data and identify nonlinear dynamical equations. Our simple approach offers improved robustness with sparse, noisy data compared to SINDy alone. We demonstrate its effectiveness on a Lotka-Volterra model, a unicycle dynamic model in simulation, and hardware data from an NVIDIA JetRacer system. We show superior performance over baselines including 20.78% improvement over SINDy and 61.92% improvement over SSR in predicting future trajectories from discovered dynamics.