Derivative-based SINDy (DSINDy): addressing the challenge of discovering governing equations from noisy data

DOI10.1016/j.cma.2023.116096arXiv2211.05918OpenAlexW4378895613MaRDI QIDQ6099213

Alireza Doostan, J. M. Wentz

Publication date: 19 June 2023

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2211.05918

zbMATH Keywords

nonlinear dynamicsdenoisingsparse regressiondata-driven modelingSINDy

Mathematics Subject Classification ID

Numerical smoothing, curve fitting (65D10) Ridge regression; shrinkage estimators (Lasso) (62J07) Convex programming (90C25) Time series analysis of dynamical systems (37M10) Linear transformations, semilinear transformations (15A04) Inverse problems involving ordinary differential equations (34A55)

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Cites Work

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• Discovering governing equations from data by sparse identification of nonlinear dynamical systems
• The Adaptive Lasso and Its Oracle Properties
• Enhancing sparsity by reweighted \(\ell _{1}\) minimization
• A tutorial on Gaussian process regression: modelling, exploring, and exploiting functions
• Sparse identification of nonlinear dynamical systems via reweighted \(\ell_1\)-regularized least squares
• Weak SINDy for partial differential equations
• Variational system identification of the partial differential equations governing the physics of pattern-formation: inference under varying fidelity and noise
• Atomic Decomposition by Basis Pursuit
• Probing the Pareto Frontier for Basis Pursuit Solutions
• Automated reverse engineering of nonlinear dynamical systems
• Analysis of Discrete Ill-Posed Problems by Means of the L-Curve
• On the Perturbation of Pseudo-Inverses, Projections and Linear Least Squares Problems
• Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations
• Robust and optimal sparse regression for nonlinear PDE models
• Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations
• Weak SINDy: Galerkin-Based Data-Driven Model Selection
• Simultaneous Identification and Denoising of Dynamical Systems
• Bayesian system ID: optimal management of parameter, model, and measurement uncertainty

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