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

arXiv: https://arxiv.org/abs/1711.05501 · HTML: https://mlsanity.com/paper/1711.05501/

## Key facts

- Cited by 140 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Nov 2017.

## Built on by (most cited first, 30 of 140)

- [PySINDy: A comprehensive Python package for robust sparse system identification](https://mlsanity.com/paper/2111.08481/) (2021)
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- [A computational framework for physics-informed symbolic regression with straightforward integration of domain knowledge](https://mlsanity.com/paper/2209.06257/) (2022)
- [Learning Sparse Nonlinear Dynamics via Mixed-Integer Optimization](https://mlsanity.com/paper/2206.00176/) (2022)
- [Reduced order modeling of parametrized systems through autoencoders and SINDy approach: continuation of periodic solutions](https://mlsanity.com/paper/2211.06786/) (2022)
- [Physics-Informed Machine Learning for Modeling and Control of Dynamical Systems](https://mlsanity.com/paper/2306.13867/) (2023)
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- [KNODE-MPC: A Knowledge-based Data-driven Predictive Control Framework for Aerial Robots](https://mlsanity.com/paper/2109.04821/) (2021)
- [SINDy-RL: Interpretable and Efficient Model-Based Reinforcement Learning](https://mlsanity.com/paper/2403.09110/) (2024)
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- [HAMLET: Graph Transformer Neural Operator for Partial Differential Equations](https://mlsanity.com/paper/2402.03541/) (2024)
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- [True Zero-Shot Inference of Dynamical Systems Preserving Long-Term Statistics](https://mlsanity.com/paper/2505.13192/) (2025)
- [DySMHO: Data-Driven Discovery of Governing Equations for Dynamical Systems via Moving Horizon Optimization](https://mlsanity.com/paper/2108.00069/) (2021)
- [Benchmarking sparse system identification with low-dimensional chaos](https://mlsanity.com/paper/2302.10787/) (2023)
- [Almost-Linear RNNs Yield Highly Interpretable Symbolic Codes in Dynamical Systems Reconstruction](https://mlsanity.com/paper/2410.14240/) (2024)
- [Physics-informed Spline Learning for Nonlinear Dynamics Discovery](https://mlsanity.com/paper/2105.02368/) (2021)
- [A Framework Based on Symbolic Regression Coupled with eXtended Physics-Informed Neural Networks for Gray-Box Learning of Equations of Motion from Data](https://mlsanity.com/paper/2305.10706/) (2023)
- [PROSE: Predicting Operators and Symbolic Expressions using Multimodal Transformers](https://mlsanity.com/paper/2309.16816/) (2023)
- [A toolkit for data-driven discovery of governing equations in high-noise regimes](https://mlsanity.com/paper/2111.04870/) (2021)
- [Convergence of uncertainty estimates in Ensemble and Bayesian sparse model discovery](https://mlsanity.com/paper/2301.12649/) (2023)
- [Learning Interpretable Hierarchical Dynamical Systems Models from Time Series Data](https://mlsanity.com/paper/2410.04814/) (2024)
- [Hybrid analysis and modeling, eclecticism, and multifidelity computing toward digital twin revolution](https://mlsanity.com/paper/2103.14629/) (2021)

## 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.