Randomized Dynamic Mode Decomposition
From MaRDI portal
Publication:5207530
DOI10.1137/18M1215013zbMath1427.65410arXiv1702.02912MaRDI QIDQ5207530
Lionel Mathelin, N. Benjamin Erichson, Steven L. Brunton, J. Nathan Kutz
Publication date: 3 January 2020
Published in: SIAM Journal on Applied Dynamical Systems (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1702.02912
Numerical solutions to overdetermined systems, pseudoinverses (65F20) Dynamical systems in fluid mechanics, oceanography and meteorology (37N10) Time series analysis of dynamical systems (37M10) Numerical problems in dynamical systems (65P99)
Related Items
Projection-tree reduced-order modeling for fast \(N\)-body computations ⋮ Modern Koopman Theory for Dynamical Systems ⋮ A dynamic mode decomposition technique for the analysis of non-uniformly sampled flow data ⋮ LaSDI: parametric latent space dynamics identification ⋮ Data-driven probability density forecast for stochastic dynamical systems ⋮ Time series, hidden variables and spatio-temporal ordinality networks ⋮ Data‐driven identification of the spatiotemporal structure of turbulent flows by streaming dynamic mode decomposition ⋮ Higher-order dynamic mode decomposition on-the-fly: a low-order algorithm for complex fluid flows ⋮ Koopman operator learning using invertible neural networks ⋮ Piecewise DMD for oscillatory and Turing spatio-temporal dynamics ⋮ Multi-scale proper orthogonal decomposition of complex fluid flows ⋮ Shallow neural networks for fluid flow reconstruction with limited sensors ⋮ Randomized linear algebra for model reduction. II: Minimal residual methods and dictionary-based approximation ⋮ Kernel methods for detecting coherent structures in dynamical data ⋮ Data-driven resolvent analysis ⋮ New robust principal component analysis for joint image alignment and recovery via affine transformations, Frobenius and \(L_{2,1}\) norms ⋮ Modes of Homogeneous Gradient Flows ⋮ Bootstrapping the operator norm in high dimensions: error estimation for covariance matrices and sketching
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions
- Compressed sensing and dynamic mode decomposition
- Lattice Boltzmann simulations of thermal convective flows in two dimensions
- Applications of the dynamic mode decomposition
- A fast immersed boundary method using a nullspace approach and multi-domain far-field boundary conditions
- The truncated SVD as a method for regularization
- The immersed boundary method: a projection approach
- On dynamic mode decomposition: theory and applications
- A New Selection Operator for the Discrete Empirical Interpolation Method---Improved A Priori Error Bound and Extensions
- Dynamic Mode Decomposition with Control
- Multiresolution Dynamic Mode Decomposition
- A Randomized Blocked Algorithm for Efficiently Computing Rank-revealing Factorizations of Matrices
- Computational Advertising: Techniques for Targeting Relevant Ads
- The Optimal Hard Threshold for Singular Values is <inline-formula> <tex-math notation="TeX">\(4/\sqrt {3}\) </tex-math></inline-formula>
- Dynamic mode decomposition of numerical and experimental data
- IMPROVED ANALYSIS OF THE SUBSAMPLED RANDOMIZED HADAMARD TRANSFORM
- Randomized Algorithms for Matrices and Data
- Extensions of Lipschitz mappings into a Hilbert space
- Deblurring Images
- Truncated Singular Value Decomposition Solutions to Discrete Ill-Posed Problems with Ill-Determined Numerical Rank
- Spectral analysis of nonlinear flows
- A Randomized Algorithm for Principal Component Analysis
- A Technique for the Numerical Solution of Certain Integral Equations of the First Kind
- The Modified Truncated SVD Method for Regularization in General Form
- A Practical Examination of Some Numerical Methods for Linear Discrete Ill-Posed Problems
- ARPACK Users' Guide
- Ergodic Theory, Dynamic Mode Decomposition, and Computation of Spectral Properties of the Koopman Operator
- Data-Driven Sparse Sensor Placement for Reconstruction: Demonstrating the Benefits of Exploiting Known Patterns
- Efficiency of randomised dynamic mode decomposition for reduced order modelling
- Subspace Iteration Randomization and Singular Value Problems
- Sparse Sensing and DMD-Based Identification of Flow Regimes and Bifurcations in Complex Flows
- Recursive dynamic mode decomposition of transient and post-transient wake flows
- Compressive-Projection Principal Component Analysis
- Turbulence, Coherent Structures, Dynamical Systems and Symmetry
- Fast monte-carlo algorithms for finding low-rank approximations