On the Compressive Spectral Method

DOI10.1137/140965909zbMath1314.65152OpenAlexW1988202149MaRDI QIDQ5251793

Hayden Schaeffer, Alan Mackey, Stanley J. Osher

Publication date: 21 May 2015

Published in: Multiscale Modeling & Simulation (Search for Journal in Brave)

Full work available at URL: https://resolver.caltech.edu/CaltechAUTHORS:20150202-095600251

zbMATH Keywords

spectral methodPDEsmultiscale methodssparse representationcompressed sensing

Mathematics Subject Classification ID

Computational methods for sparse matrices (65F50) Numerical optimization and variational techniques (65K10) Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Iterative numerical methods for linear systems (65F10)

Related Items (15)

Compressed vibration modes of elastic bodies ⋮ Compressed sensing and dynamic mode decomposition ⋮ Extracting Sparse High-Dimensional Dynamics from Limited Data ⋮ Sparsity enabled cluster reduced-order models for control ⋮ Hidden physics models: machine learning of nonlinear partial differential equations ⋮ Online Interpolation Point Refinement for Reduced-Order Models using a Genetic Algorithm ⋮ Data-Driven Identification of Parametric Partial Differential Equations ⋮ Extracting Structured Dynamical Systems Using Sparse Optimization With Very Few Samples ⋮ A Compressive Spectral Collocation Method for the Diffusion Equation Under the Restricted Isometry Property ⋮ Learning partial differential equations via data discovery and sparse optimization ⋮ A Gradient-Enhanced L1 Approach for the Recovery of Sparse Trigonometric Polynomials ⋮ Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations ⋮ Sparse + low-energy decomposition for viscous conservation laws ⋮ Sparse recovery in bounded Riesz systems with applications to numerical methods for PDEs ⋮ Discovering governing equations from data by sparse identification of nonlinear dynamical systems

Uses Software

• PDCO
• PhaseLift

Cites Work

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• Generation of Semi-Groups of Nonlinear Transformations on General Banach Spaces
• Phase Retrieval via Matrix Completion
• Compressed sensing

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