Robust and optimal sparse regression for nonlinear PDE models

DOI10.1063/1.5120861zbMath1433.35387arXiv1907.09507OpenAlexW2979458970WikidataQ91058109 ScholiaQ91058109MaRDI QIDQ4972990

Roman O. Grigoriev, Patrick A. K. Reinbold, Daniel R. Gurevich

Publication date: 29 November 2019

Published in: Chaos: An Interdisciplinary Journal of Nonlinear Science (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1907.09507

zbMATH Keywords

weak formulationnoisy datanonlinear partial differential equationssparse regression4th-order Kuramoto-Sivashinsky equation

Mathematics Subject Classification ID

Ridge regression; shrinkage estimators (Lasso) (62J07) Robustness and adaptive procedures (parametric inference) (62F35) Numerical solutions to overdetermined systems, pseudoinverses (65F20) Eigenvalues, singular values, and eigenvectors (15A18) PDEs in connection with statistics (35Q62)

Related Items (9)

Weak SINDy for partial differential equations ⋮ Deep-learning based discovery of partial differential equations in integral form from sparse and noisy data ⋮ Data-driven discovery of governing equations for transient heat transfer analysis ⋮ Robust Identification of Differential Equations by Numerical Techniques from a Single Set of Noisy Observation ⋮ Learning sparse nonlinear dynamics via mixed-integer optimization ⋮ Direct estimation of parameters in ODE models using WENDy: weak-form estimation of nonlinear dynamics ⋮ Derivative-based SINDy (DSINDy): addressing the challenge of discovering governing equations from noisy data ⋮ Parsimony as the ultimate regularizer for physics-informed machine learning ⋮ WeakIdent: weak formulation for identifying differential equation using narrow-fit and trimming

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