SINDy-PI: A Robust Algorithm for Parallel Implicit Sparse Identification of Nonlinear Dynamics

Abstract

Accurately modeling the nonlinear dynamics of a system from measurement data is a challenging yet vital topic. The sparse identification of nonlinear dynamics (SINDy) algorithm is one approach to discover dynamical systems models from data. Although extensions have been developed to identify implicit dynamics, or dynamics described by rational functions, these extensions are extremely sensitive to noise. In this work, we develop SINDy-PI (parallel, implicit), a robust variant of the SINDy algorithm to identify implicit dynamics and rational nonlinearities. The SINDy-PI framework includes multiple optimization algorithms and a principled approach to model selection. We demonstrate the ability of this algorithm to learn implicit ordinary and partial differential equations and conservation laws from limited and noisy data. In particular, we show that the proposed approach is several orders of magnitude more noise robust than previous approaches, and may be used to identify a class of complex ODE and PDE dynamics that were previously unattainable with SINDy, including for the double pendulum dynamics and the Belousov Zhabotinsky (BZ) reaction.

25 pages, 9 figures, 5 tables

References in corpus (4)

• Hidden Physics Models: Machine Learning of Nonlinear Partial Differential Equations
• Applied Koopmanism
• Using Noisy or Incomplete Data to Discover Models of Spatiotemporal Dynamics
• Sparse Identification for Nonlinear Optical Communication Systems: SINO Method

Cited by in corpus (41)

• Physics-informed learning of governing equations from scarce data
• Ensemble-SINDy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and control
• Uncertainty Quantification in Machine Learning for Engineering Design and Health Prognostics: A Tutorial
• PySINDy: A comprehensive Python package for robust sparse system identification
• Physics-constrained, low-dimensional models for MHD: First-principles and data-driven approaches
• Bayesian Parameter Estimation for Dynamical Models in Systems Biology
• Sparse Identification of Nonlinear Dynamical Systems via Reweighted ${\ell }_1$-regularized Least Squares
• Applications and Techniques for Fast Machine Learning in Science
• $\text{FastSVD-ML-ROM}$: A Reduced-Order Modeling Framework based on Machine Learning for Real-Time Applications
• Discovering Sparse Interpretable Dynamics from Partial Observations
• Data-Driven Equation Discovery of a Cloud Cover Parameterization
• Discovery of partial differential equations from highly noisy and sparse data with physics-informed information criterion
• WeakIdent: Weak formulation for Identifying Differential Equations using Narrow-fit and Trimming
• Permanent magnet optimization for stellarators as sparse regression
• Dynamical System Identification, Model Selection and Model Uncertainty Quantification by Bayesian Inference
• Learning fluid physics from highly turbulent data using sparse physics-informed discovery of empirical relations (SPIDER)
• Data-Driven Stabilization of Periodic Orbits
• Deep Learning of Conjugate Mappings
• Auxiliary Functions as Koopman Observables: Data-Driven Analysis of Dynamical Systems via Polynomial Optimization
• Data-driven Discovery of Delay Differential Equations with Discrete Delays
• Data-driven discovery of a heat flux closure for electrostatic plasma phenomena
• Estimating covariant Lyapunov vectors from data
• The Experimental Multi-Arm Pendulum on a Cart: A Benchmark System for Chaos, Learning, and Control
• Promoting global stability in data-driven models of quadratic nonlinear dynamics
• Multi-objective discovery of PDE systems using evolutionary approach
• Stepwise Model Reconstruction of Robotic Manipulator Based on Data-Driven Method
• Uncovering Closed-form Governing Equations of Nonlinear Dynamics from Videos
• BINDy -- Bayesian identification of nonlinear dynamics with reversible-jump Markov-chain Monte-Carlo
• CTSR: Cartesian tensor-based sparse regression for data-driven discovery of high-dimensional invariant governing equations
• Constrained or Unconstrained? Neural-Network-Based Equation Discovery from Data
• Data-driven discovery of mechanical models directly from MRI spectral data
• Sparse system identification by low-rank approximation
• Data-driven model reconstruction for nonlinear wave dynamics
• Physics-informed Spline Learning for Nonlinear Dynamics Discovery
• Inferring the Structure of Ordinary Differential Equations
• OKRidge: Scalable Optimal k-Sparse Ridge Regression
• Grammar-based Ordinary Differential Equation Discovery
• Embedding physical symmetries into machine-learned reduced plasma physics models via data augmentation
• The Machine Learning Approach to Moment Closure Relations for Plasma: A Review
• Reconstruction of observed mechanical motions with Artificial Intelligence tools
• Relaxation dynamics of a quantum spin coupled to a topological edge state