mlsanityData to 7 Oct 2026

Sparse identification of nonlinear dynamics for model predictive control in the low-data limit

arXiv 1711.05501 ↗First posted 15 Nov 2017math.OC math.DS physics.data-ancited by 139

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Abstract (arXiv)

The data-driven discovery of dynamics via machine learning is currently pushing the frontiers of modeling and control efforts, and it provides a tremendous opportunity to extend the reach of model predictive control. However, many leading methods in machine learning, such as neural networks, require large volumes of training data, may not be interpretable, do not easily include known constraints and symmetries, and often do not generalize beyond the attractor where models are trained. These factors limit the use of these techniques for the online identification of a model in the low-data limit, for example following an abrupt change to the system dynamics. In this work, we extend the recent sparse identification of nonlinear dynamics (SINDY) modeling procedure to include the effects of actuation and demonstrate the ability of these models to enhance the performance of model predictive control (MPC), based on limited, noisy data. SINDY models are parsimonious, identifying the fewest terms in the model needed to explain the data, making them interpretable, generalizable, and reducing the burden of training data. We show that the resulting SINDY-MPC framework has higher performance, requires significantly less data, and is more computationally efficient and robust to noise than neural network models, making it viable for online training and execution in response to rapid changes to the system. SINDY-MPC also shows improved performance over linear data-driven models, although linear models may provide a stopgap until enough data is available for SINDY. SINDY-MPC is demonstrated on a variety of dynamical systems with different challenges, including the chaotic Lorenz system, a simple model for flight control of an F8 aircraft, and an HIV model incorporating drug treatment.

Key facts. Cited by 139 papers in the map (data through 7 Oct 2026). First posted on arXiv 15 Nov 2017.

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Citing papers per year: 2021: 16; 2022: 20; 2023: 29; 2024: 28; 2025: 25; 2026: 21.

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  1. 2021PySINDy: A comprehensive Python package for robust sparse system identificationcited by 88
  2. 2023Machine learning with data assimilation and uncertainty quantification for dynamical systems: a reviewcited by 74
  3. 2023Transformer-based Planning for Symbolic Regressioncited by 72
  4. 2022Discovering Governing Equations from Partial Measurements with Deep Delay Autoencoderscited by 58
  5. 2024KAN-ODEs: Kolmogorov-Arnold Network Ordinary Differential Equations for Learning Dynamical Systems and Hidden Physicscited by 58
  6. 2021Physics-Guided Deep Learning for Dynamical Systems: A Surveycited by 43
  7. 2021Deeptime: a Python library for machine learning dynamical models from time series datacited by 36
  8. 2024Out-of-Domain Generalization in Dynamical Systems Reconstructioncited by 33
  9. 2022A computational framework for physics-informed symbolic regression with straightforward integration of domain knowledgecited by 31
  10. 2022Learning Sparse Nonlinear Dynamics via Mixed-Integer Optimizationcited by 29
  11. 2022Reduced order modeling of parametrized systems through autoencoders and SINDy approach: continuation of periodic solutionscited by 29
  12. 2023Physics-Informed Machine Learning for Modeling and Control of Dynamical Systemscited by 28
38 more
  1. 2021Structure-preserving Sparse Identification of Nonlinear Dynamics for Data-driven Modelingcited by 27
  2. 2021KNODE-MPC: A Knowledge-based Data-driven Predictive Control Framework for Aerial Robotscited by 26
  3. 2022Bayesian autoencoders for data-driven discovery of coordinates, governing equations and fundamental constantscited by 24
  4. 2024HAMLET: Graph Transformer Neural Operator for Partial Differential Equationscited by 24
  5. 2024SINDy-RL: Interpretable and Efficient Model-Based Reinforcement Learningcited by 24
  6. 2021Robust discovery of partial differential equations in complex situationscited by 21
  7. 2025True Zero-Shot Inference of Dynamical Systems Preserving Long-Term Statisticscited by 20
  8. 2021DySMHO: Data-Driven Discovery of Governing Equations for Dynamical Systems via Moving Horizon Optimizationcited by 19
  9. 2022Deep Reinforcement Learning for Adaptive Mesh Refinementcited by 19
  10. 2023Benchmarking sparse system identification with low-dimensional chaoscited by 19
  11. 2021Physics-informed Spline Learning for Nonlinear Dynamics Discoverycited by 18
  12. 2023A Framework Based on Symbolic Regression Coupled with eXtended Physics-Informed Neural Networks for Gray-Box Learning of Equations of Motion from Datacited by 18
  13. 2024Almost-Linear RNNs Yield Highly Interpretable Symbolic Codes in Dynamical Systems Reconstructioncited by 18
  14. 2023PROSE: Predicting Operators and Symbolic Expressions using Multimodal Transformerscited by 16
  15. 2021A toolkit for data-driven discovery of governing equations in high-noise regimescited by 15
  16. 2023Convergence of uncertainty estimates in Ensemble and Bayesian sparse model discoverycited by 15
  17. 2021Hybrid analysis and modeling, eclecticism, and multifidelity computing toward digital twin revolutioncited by 14
  18. 2022DeepGraphONet: A Deep Graph Operator Network to Learn and Zero-shot Transfer the Dynamic Response of Networked Systemscited by 14
  19. 2024Learning Interpretable Hierarchical Dynamical Systems Models from Time Series Datacited by 14
  20. 2022Online Weak-form Sparse Identification of Partial Differential Equationscited by 13
  21. 2024Koopman-Assisted Reinforcement Learningcited by 11
  22. 2022Random Feature Models for Learning Interacting Dynamical Systemscited by 10
  23. 2023How to Learn and Generalize From Three Minutes of Data: Physics-Constrained and Uncertainty-Aware Neural Stochastic Differential Equationscited by 10
  24. 2024ADAM-SINDy: An Efficient Optimization Framework for Parameterized Nonlinear Dynamical System Identificationcited by 10
  25. 2024Dynamical System Identification, Model Selection and Model Uncertainty Quantification by Bayesian Inferencecited by 9
  26. 2024From Fourier to Neural ODEs: Flow Matching for Modeling Complex Systemscited by 9
  27. 2022On the sample complexity of stabilizing linear dynamical systems from datacited by 8
  28. 2022Deep learning delay coordinate dynamics for chaotic attractors from partial observable datacited by 8
  29. 2023A Bayesian Framework for learning governing Partial Differential Equation from Datacited by 8
  30. 2023RSRM: Reinforcement Symbolic Regression Machinecited by 7
  31. 2024Parametric PDE Control with Deep Reinforcement Learning and Differentiable L0-Sparse Polynomial Policiescited by 7
  32. 2024Modeling Unknown Stochastic Dynamical System Subject to External Excitationcited by 7
  33. 2023Discovering stochastic partial differential equations from limited data using variational Bayes inferencecited by 6
  34. 2023A Robust SINDy Approach by Combining Neural Networks and an Integral Formcited by 6
  35. 2023Discussing the Spectrum of Physics-Enhanced Machine Learning; a Survey on Structural Mechanics Applicationscited by 6
  36. 2025Improving Monte Carlo Tree Search for Symbolic Regressioncited by 6
  37. 2021On the Universal Transformation of Data-Driven Models to Control Systemscited by 5
  38. 2022Bounded nonlinear forecasts of partially observed geophysical systems with physics-constrained deep learningcited by 5

50 most cited of 139 All 139 (JSON)