mlsanityData to 7 Oct 2026

Symbolic Regression on Sparse and Noisy Data with Gaussian Processes

arXiv 2309.11076 ↗First posted 20 Sep 2023cs.LG cs.SY eess.SYcited by 4

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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.

Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Builds on 12 of its 22 references that are in the map. First posted on arXiv 20 Sep 2023.

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12 of 22 references.

References · 12

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2018Neural Ordinary Differential Equationscited by 3,733
  3. 2020Physics-informed learning of governing equations from scarce datacited by 167
  4. 2017Machine Learning of Linear Differential Equations using Gaussian Processescited by 139
  5. 2017Sparse identification of nonlinear dynamics for model predictive control in the low-data limitcited by 139
  6. 2021Ensemble-SINDy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and controlcited by 134
  7. 2020SINDy-PI: A Robust Algorithm for Parallel Implicit Sparse Identification of Nonlinear Dynamicscited by 125
  8. 2017Sparse learning of stochastic dynamic equationscited by 76
  9. 2018Learning unknown ODE models with Gaussian processescited by 54
  10. 2020Automatic Differentiation to Simultaneously Identify Nonlinear Dynamics and Extract Noise Probability Distributions from Datacited by 36
  11. 2020Sparse Identification of Nonlinear Dynamical Systems via Reweighted ℓ1-regularized Least Squarescited by 21
  12. 2019Modeling, Identification and Control of Model Jet Engines for Jet Powered Roboticscited by 5

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 1; 2026: 3.

4 papers.

  1. 2025A Weak Penalty Neural ODE for Learning Chaotic Dynamics from Noisy Time Seriescited by 1
  2. 2026Machine Learning Hamiltonian Dynamical Systems with Sparse and Noisy Datacited by 1
  3. 2026Knowledge-Informed Kernel State Reconstruction from Heterogeneous Partial Observationscited by 0
  4. 2026Data Enrichment for Symbolic Regression Using Diffusion Modelscited by 0