Symbolic Regression on Sparse and Noisy Data with Gaussian Processes
This addresses the challenge of symbolic regression for dynamical systems with limited data, which is incremental as it builds on existing SINDy methods.
The paper tackles the problem of deriving dynamical models from sparse and noisy data by combining Gaussian process regression with SINDy, resulting in over 50% improvement in predicting future trajectories compared to baselines.
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 approach GPSINDy offers improved robustness with sparse, noisy data compared to SINDy alone. We demonstrate its effectiveness on simulation data from Lotka-Volterra and unicycle models and hardware data from an NVIDIA JetRacer system. We show superior performance over baselines including more than 50% improvement over SINDy and other baselines in predicting future trajectories from noise-corrupted and sparse 5 Hz data.