Symbolic Regression on Sparse and Noisy Data with Gaussian Processes

• URL: http://arxiv.org/abs/2309.11076v3
• Date: Thu, 10 Oct 2024 22:47:13 GMT
• Title: Symbolic Regression on Sparse and Noisy Data with Gaussian Processes
• Authors: Junette Hsin, Shubhankar Agarwal, Adam Thorpe, Luis Sentis, David Fridovich-Keil,
• Abstract summary: GPSINDy offers improved robustness with sparse, noisy data compared to SINDy alone. We show superior performance over baselines including more than 50% improvement over SINDy.
• Score: 11.413977318301903
• License: http://creativecommons.org/licenses/by/4.0/
• 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 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.

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