# Symbolic Regression on Sparse and Noisy Data with Gaussian Processes

arXiv: https://arxiv.org/abs/2309.11076 · HTML: https://mlsanity.com/paper/2309.11076/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 22 references that are in the map.
- First posted on arXiv 20 Sep 2023.

## Builds on (most cited first, 12 of 12)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Physics-informed learning of governing equations from scarce data](https://mlsanity.com/paper/2005.03448/) (2020)
- [Machine Learning of Linear Differential Equations using Gaussian Processes](https://mlsanity.com/paper/1701.02440/) (2017)
- [Sparse identification of nonlinear dynamics for model predictive control in the low-data limit](https://mlsanity.com/paper/1711.05501/) (2017)
- [Ensemble-SINDy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and control](https://mlsanity.com/paper/2111.10992/) (2021)
- [SINDy-PI: A Robust Algorithm for Parallel Implicit Sparse Identification of Nonlinear Dynamics](https://mlsanity.com/paper/2004.02322/) (2020)
- [Sparse learning of stochastic dynamic equations](https://mlsanity.com/paper/1712.02432/) (2017)
- [Learning unknown ODE models with Gaussian processes](https://mlsanity.com/paper/1803.04303/) (2018)
- [Automatic Differentiation to Simultaneously Identify Nonlinear Dynamics and Extract Noise Probability Distributions from Data](https://mlsanity.com/paper/2009.08810/) (2020)
- [Sparse Identification of Nonlinear Dynamical Systems via Reweighted ℓ1-regularized Least Squares](https://mlsanity.com/paper/2005.13232/) (2020)
- [Modeling, Identification and Control of Model Jet Engines for Jet Powered Robotics](https://mlsanity.com/paper/1909.13296/) (2019)

## Built on by (most cited first, 4 of 4)

- [A Weak Penalty Neural ODE for Learning Chaotic Dynamics from Noisy Time Series](https://mlsanity.com/paper/2511.06609/) (2025)
- [Machine Learning Hamiltonian Dynamical Systems with Sparse and Noisy Data](https://mlsanity.com/paper/2604.17470/) (2026)
- [Knowledge-Informed Kernel State Reconstruction from Heterogeneous Partial Observations](https://mlsanity.com/paper/2601.22328/) (2026)
- [Data Enrichment for Symbolic Regression Using Diffusion Models](https://mlsanity.com/paper/2606.00988/) (2026)

## Abstract (arXiv)

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.