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Colbrook, Matthew J.

  1. Rigorous data-driven computation of spectral properties of Koopman operators for dynamical systems
    2021/11/29 by Matthew J. Colbrook, Alex Townsend, Colbrook, Matthew J. +1 · 16 citations
    Computer Science · Engineering · Physics and Astronomy · #37A30 #37M10 #37N10 #37N25 #47A10 #47B33 #65F99 #65P99 #65T99 #Computational Fluid Dynamics and Aerodynamics #Dynamical Systems (math.DS) #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Turbulent Flows #Gaussian Processes and Bayesian Inference #Machine Learning (cs.LG) #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Spectral Theory (math.SP)
  2. The Multiverse of Dynamic Mode Decomposition Algorithms
    2023/11/30 by Colbrook, Matthew J. · 11 citations
    #Dynamical Systems (math.DS) #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Numerical Analysis (math.NA) #Spectral Theory (math.SP)
  3. The mpEDMD Algorithm for Data-Driven Computations of Measure-Preserving Dynamical Systems
    2022/09/06 by Matthew J. Colbrook, Colbrook, Matthew J. · 7 citations
    Physics and Astronomy · Earth and Planetary Sciences · Engineering · #Model Reduction and Neural Networks #Meteorological Phenomena and Simulations #Fluid Dynamics and Turbulent Flows
  4. The foundations of spectral computations via the Solvability Complexity Index hierarchy
    2019/08/26 by Matthew J. Colbrook, Colbrook, Matthew J., Anders C. Hansen +1 · 4 citations
    Computer Science · #35P15 #46N40 #47A10 #65L15 #65N25 #FOS: Mathematics #Matrix Theory and Algorithms #Spectral Theory (math.SP) #Topological and Geometric Data Analysis
  5. Computing semigroups with error control
    2021/10/12 by Colbrook, Matthew J. · 3 citations
    #46N40 #47A10 #65J08 #65M15 #65N35 #FOS: Mathematics #Numerical Analysis (math.NA)
  6. Rigged Dynamic Mode Decomposition: Data-Driven Generalized Eigenfunction Decompositions for Koopman Operators
    2024/05/01 by Matthew J. Colbrook, Catherine Drysdale, Colbrook, Matthew J. +3 · 6 citations
    Physics and Astronomy · Engineering · #Model Reduction and Neural Networks #Fluid Dynamics and Vibration Analysis #Machine Fault Diagnosis Techniques
  7. Beyond expectations: Residual Dynamic Mode Decomposition and Variance for Stochastic Dynamical Systems
    2023/08/21 by Colbrook, Matthew J., Li, Qin, Raut, Ryan V. +1 · 4 citations
    #37H99 #37M10 #37N25 #47A10 #47B33 #65P99 #Chaotic Dynamics (nlin.CD) #Dynamical Systems (math.DS) #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Machine Learning (cs.LG) #Numerical Analysis (math.NA) #Spectral Theory (math.SP)
  8. Limits and Powers of Koopman Learning
    2024/07/08 by Colbrook, Matthew J., Mezić, Igor, Stepanenko, Alexei · 5 citations
    #Dynamical Systems (math.DS) #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Numerical Analysis (math.NA) #Optimization and Control (math.OC) #Spectral Theory (math.SP)
  9. Computing spectral properties of topological insulators without artificial truncation or supercell approximation
    2021/12/07 by Colbrook, Matthew J., Horning, Andrew, Thicke, Kyle +1 · 2 citations
    #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Numerical Analysis (math.NA) #Spectral Theory (math.SP)
  10. Avoiding discretization issues for nonlinear eigenvalue problems
    2023/05/02 by Matthew J. Colbrook, Colbrook, Matthew J., Alex Townsend +1 · 2 citations
    Computer Science · Mathematics · #35P30 #47A10 #65N25 #65N30 #Advanced Optimization Algorithms Research #FOS: Electrical engineering #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Numerical methods for differential equations #Spectral Theory (math.SP) #Systems and Control (eess.SY) #electronic engineering #information engineering
  11. Computing spectral measures of self-adjoint operators
    2020/06/02 by Colbrook, Matthew J., Horning, Andrew, Townsend, Alex · 2 citations
    #46N40 #47A10 #47N50 #65N35 #81Q10 #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #Numerical Analysis (math.NA) #Spectral Theory (math.SP)
  12. Another look at Residual Dynamic Mode Decomposition in the regime of fewer Snapshots than Dictionary Size
    2024/03/09 by Matthew J. Colbrook, Colbrook, Matthew J. · 3 citations
    Chemical Engineering · #Advanced Combustion Engine Technologies #Chaotic Dynamics (nlin.CD) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Numerical Analysis (math.NA) #Optimization and Control (math.OC) #Spectral Theory (math.SP)
  13. Restarts subject to approximate sharpness: A parameter-free and optimal scheme for first-order methods
    2023/01/05 by Ben Adcock, Matthew J. Colbrook, Adcock, Ben +3 · 1 citation
    Computer Science · Engineering · #65B99 #65K0 #68Q25 #90C25 #90C60 #Computer Vision and Pattern Recognition (cs.CV) #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Numerical Analysis (math.NA) #Optimization and Control (math.OC) #Photoacoustic and Ultrasonic Imaging #Sparse and Compressive Sensing Techniques #Stochastic Gradient Optimization Techniques
  14. Multiplicative Dynamic Mode Decomposition
    2024/05/08 by Boullé, Nicolas, Colbrook, Matthew J. · 2 citations
    #Dynamical Systems (math.DS) #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Numerical Analysis (math.NA) #Optimization and Control (math.OC) #Spectral Theory (math.SP)
  15. On the Convergence of Hermitian Dynamic Mode Decomposition
    2024/01/06 by Nicolas Boullé, Matthew J. Colbrook, Boullé, Nicolas +1 · 1 citation
    Engineering · #Dynamical Systems (math.DS) #Dynamics and Control of Mechanical Systems #FOS: Computer and information sciences #FOS: Mathematics #Fluid Dynamics Simulations and Interactions #Machine Learning (cs.LG) #Numerical Analysis (math.NA) #Spectral Theory (math.SP) #Vehicle Dynamics and Control Systems
  16. Computing Generalized Eigenfunctions in Rigged Hilbert Spaces
    2024/10/10 by Matthew J. Colbrook, Andrew Horning, Colbrook, Matthew J. +2 · 2 citations
    Computer Science · Mathematics · #Matrix Theory and Algorithms #Advanced Topics in Algebra
  17. Optimal Algorithms for Quantifying Spectral Size with Applications to Quasicrystals
    2024/07/29 by Colbrook, Matthew J., Embree, Mark, Fillman, Jake · 1 citation
    #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical Analysis (math.NA) #Spectral Theory (math.SP)
  18. An Introductory Guide to Koopman Learning
    2025/10/24 by Colbrook, Matthew J., Drmač, Zlatko, Horning, Andrew · 2 citations
    #Dynamical Systems (math.DS) #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Numerical Analysis (math.NA) #Optimization and Control (math.OC) #Spectral Theory (math.SP)
  19. Convergent Methods for Koopman Operators on Reproducing Kernel Hilbert Spaces
    2025/06/18 by Boullé, Nicolas, Loiseau, Jean-Christophe, Colbrook, Matthew J. +3 · 4 citations
    Physics and Astronomy · Computer Science · #Model Reduction and Neural Networks #Quantum many-body systems #Advanced Graph Neural Networks