Ensemble-SINDy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and control

Abstract

Sparse model identification enables the discovery of nonlinear dynamical systems purely from data; however, this approach is sensitive to noise, especially in the low-data limit. In this work, we leverage the statistical approach of bootstrap aggregating (bagging) to robustify the sparse identification of nonlinear dynamics (SINDy) algorithm. First, an ensemble of SINDy models is identified from subsets of limited and noisy data. The aggregate model statistics are then used to produce inclusion probabilities of the candidate functions, which enables uncertainty quantification and probabilistic forecasts. We apply this ensemble-SINDy (E-SINDy) algorithm to several synthetic and real-world data sets and demonstrate substantial improvements to the accuracy and robustness of model discovery from extremely noisy and limited data. For example, E-SINDy uncovers partial differential equations models from data with more than twice as much measurement noise as has been previously reported. Similarly, E-SINDy learns the Lotka Volterra dynamics from remarkably limited data of yearly lynx and hare pelts collected from 1900-1920. E-SINDy is computationally efficient, with similar scaling as standard SINDy. Finally, we show that ensemble statistics from E-SINDy can be exploited for active learning and improved model predictive control.

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Cited by in corpus (30)

• PySINDy: A comprehensive Python package for robust sparse system identification
• KAN-ODEs: Kolmogorov-Arnold Network Ordinary Differential Equations for Learning Dynamical Systems and Hidden Physics
• DySMHO: Data-Driven Discovery of Governing Equations for Dynamical Systems via Moving Horizon Optimization
• Derivative-based SINDy (DSINDy): Addressing the challenge of discovering governing equations from noisy data
• EKF-SINDy: Empowering the extended Kalman filter with sparse identification of nonlinear dynamics
• Direct Estimation of Parameters in ODE Models Using WENDy: Weak-form Estimation of Nonlinear Dynamics
• Hypergraph reconstruction from dynamics
• Noise-aware Physics-informed Machine Learning for Robust PDE Discovery
• Learning Anisotropic Interaction Rules from Individual Trajectories in a Heterogeneous Cellular Population
• Dynamical System Identification, Model Selection and Model Uncertainty Quantification by Bayesian Inference
• Deep Kernel Learning of Dynamical Models from High-Dimensional Noisy Data
• Rheo-SINDy: Finding a Constitutive Model from Rheological Data for Complex Fluids Using Sparse Identification for Nonlinear Dynamics
• CEBoosting: Online Sparse Identification of Dynamical Systems with Regime Switching by Causation Entropy Boosting
• TorchSISSO: A PyTorch-Based Implementation of the Sure Independence Screening and Sparsifying Operator for Efficient and Interpretable Model Discovery
• SINDy-RL: Interpretable and Efficient Model-Based Reinforcement Learning
• Influence of initial conditions on data-driven model identification and information entropy for ideal mhd problems
• Evolutionary Optimization of Physics-Informed Neural Networks: Evo-PINN Frontiers and Opportunities
• Identification of Forced Oscillation Sources in Wind Farms using E-SINDy
• System identification based on characteristic curves: a mathematical connection between power series and Fourier analysis for first-order nonlinear systems
• Data-driven sparse modeling of oscillations in plasma space propulsion
• Learning dynamics on invariant measures using PDE-constrained optimization
• Statistical Mechanics of Dynamical System Identification
• Challenges in identifying simple pattern-forming mechanisms in the development of settlements using demographic data
• Enhancing model identification with SINDy via nullcline reconstruction
• BINDy -- Bayesian identification of nonlinear dynamics with reversible-jump Markov-chain Monte-Carlo
• Unsupervised Constitutive Model Discovery from Sparse and Noisy Data
• Remote Manipulation of Multiple Objects with Airflow Field Using Model-Based Learning Control
• OKRidge: Scalable Optimal k-Sparse Ridge Regression
• Sparse Identification for bifurcating phenomena in Computational Fluid Dynamics
• Hyperparameter Optimization in the Estimation of PDE and Delay-PDE models from data