Weak SINDy for partial differential equations

DOI10.1016/j.jcp.2021.110525OpenAlexW3040454512WikidataQ115350069 ScholiaQ115350069MaRDI QIDQ2132599

Daniel A. Messenger, David M. Bortz

Publication date: 28 April 2022

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2007.02848

zbMATH Keywords

Galerkin methodconvolutionweak solutionspartial differential equationssparse recoverydata-driven model selection

Mathematics Subject Classification ID

Numerical methods for ordinary differential equations (65Lxx) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx) Approximation methods and numerical treatment of dynamical systems (37Mxx)

Related Items (16)

Learning mean-field equations from particle data using WSINDy ⋮ Data-driven sparse identification of nonlinear dynamical systems using linear multistep methods ⋮ Model selection via reweighted partial sparse recovery ⋮ Learning sparse nonlinear dynamics via mixed-integer optimization ⋮ Auxiliary functions as Koopman observables: data-driven analysis of dynamical systems via polynomial optimization ⋮ Direct estimation of parameters in ODE models using WENDy: weak-form estimation of nonlinear dynamics ⋮ Group projected subspace pursuit for identification of variable coefficient differential equations (GP-IDENT) ⋮ Derivative-based SINDy (DSINDy): addressing the challenge of discovering governing equations from noisy data ⋮ GPLaSDI: Gaussian process-based interpretable latent space dynamics identification through deep autoencoder ⋮ Structured model selection via ℓ1−ℓ2 optimization ⋮ Data-driven learning of differential equations: combining data and model uncertainty ⋮ Determination of the polynomial restoring force of a one DoF bistable Duffing oscillator by linear regression ⋮ Towards discovery of the differential equations ⋮ WeakIdent: weak formulation for identifying differential equation using narrow-fit and trimming ⋮ Design of the monodomain model by artificial neural networks ⋮ Stabilized neural ordinary differential equations for long-time forecasting of dynamical systems

Uses Software

• GitHub
• PySINDy
• PDE-Net

Cites Work

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