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Published Journal Articles (chronological order)

Articles that have won prizes have them highlighted in orange, and articles that have been featured on journal covers are highlighted in red.

35. M. Colbrook "The Multiverse of Dynamic Mode Decomposition Algorithms" Handbook of Numerical Analysis, to appear.
34. M. Colbrook, Q. Li, R. Raut, A. Townsend, "Beyond expectations: Residual Dynamic Mode Decomposition and Variance for Stochastic Dynamical Systems" Nonlinear Dynamics, to appear.
33. M. Colbrook, A. Townsend, "Rigorous data-driven computation of spectral properties of Koopman operators for dynamical systems" Communications on Pure and Applied Mathematics, 77(1), 2024.
32. S. Brunton, M. Colbrook, "Resilient Data-driven Dynamical Systems with Koopman: An Infinite-dimensional Numerical Analysis Perspective," SIAM News, 56(1), 2023 (cover article) pdf journal link
31. M. Colbrook, "The mpEDMD Algorithm for Data-Driven Computations of Measure-Preserving Dynamical Systems," SIAM Journal on Numerical Analysis, 61(3), 2023.
30. M. Colbrook, L. Ayton, M. Szőke, "Residual Dynamic Mode Decomposition: Robust and verified Koopmanism," Journal of Fluid Mechanics, 955, 2023.
29. M. Colbrook, A. Horning, K. Thicke, A. Watson, "Computing spectral properties of topological insulators without artificial truncation or supercell approximation," IMA Journal of Applied Mathematics, 88(1), 2023.
28. M. Colbrook, V. Antun, A. Hansen, "The difficulty of computing stable and accurate neural networks: On the barriers of deep learning and Smale's 18th problem," Proc. Nat. Acad. USA, 119.12, 2022.

Interview for IEEE spectrum (world's leading engineering magazine, flagship publication of the IEEE): Some AI systems may be impossible to compute
We made the cover of SIAM News: Proving Existence Is Not Enough: Mathematical Paradoxes Unravel the Limits of Neural Networks in Artificial Intelligence
Cambridge press release: Mathematical paradox demonstrates the limits of AI
27. V. Antun, M. Colbrook, A. Hansen, "Proving Existence Is Not Enough: Mathematical Paradoxes Unravel the Limits of Neural Networks in Artificial Intelligence," SIAM News, 55(4), 2022 (cover article) pdf journal link
26. M. Colbrook, V. Antun, A. Hansen, "Mathematical paradoxes unearth the boundaries of AI," TheScienceBreaker, 2022.
25. M. Colbrook, "On the computation of geometric features of spectra of linear operators on Hilbert spaces," Foundations of Computational Mathematics, to appear.
24. M. Colbrook, A. Hansen, "The foundations of spectral computations via the solvability complexity index hierarchy," Journal of the European Mathematical Society, to appear.
23. M. Colbrook, "WARPd: A linearly convergent first-order method for inverse problems with approximate sharpness conditions," SIAM Journal on Imaging Sciences, 15(3), 1539-1575, 2022. pdf journal link
22. D. Johnstone, M. Colbrook, A. Nielsen, P. Öhberg, C. Duncan, "Bulk Localised Transport States in Infinite and Finite Quasicrystals via Magnetic Aperiodicity," Physical Review B, 106(4), 2022. (Editors' Suggestion)
21. M. Colbrook, "Computing semigroups with error control," SIAM Journal on Numerical Analysis, 60(1), 396-422, 2022.
An IMA Leslie Fox Prize 2023
20. M. Colbrook, L. Ayton, "A contour method for time-fractional PDEs and an application to fractional viscoelastic beam equations," Journal of Computational Physics, 454, 2022.
19. T. Loss, M. Colbrook, A. Hansen, "Stratified sampling based compressed sensing for structured signals," IEEE Transactions on Signal Processing, 70, 3530-3539, 2022.
18. M. Colbrook, A. Horning, A. Townsend, "Computing spectral measures of self-adjoint operators," SIAM Review, 63(3), 489-524, 2021 (cover article)
SIAM Activity Group on Computational Science and Engineering Best Paper Prize 2023
17. M. Colbrook, "Computing spectral measures and spectral types," Communications in Mathematical Physics, 384, 433-501, 2021.
16. M. Colbrook, "Unscrambling the Infinite: Can we Compute Spectra?," IMA Mathematics Today, June 2021. pdf journal link
15. M. Colbrook, L. Ayton, "Do we need non-linear corrections? On the boundary Forchheimer equation in acoustic scattering," Journal of Sound and Vibration, 495, 115905, 2021.
14. L. Ayton, M. Colbrook, T. Geyer, P. Chaitanya, E. Sarradj, "Reducing aerofoil-turbulence interaction noise through chordwise-varying porosity," Journal of Fluid Mechanics, 906, 2021.
13. M. Colbrook, A. Kisil, "A Mathieu function boundary spectral method for diffraction by multiple variable poro-elastic plates, with applications to metamaterials and acoustics," Proceedings of the Royal Society A, 476(2241), 20200184, 2020. (cover article for special issue)
12. M. Colbrook, Z. Botev, K. Kuritz, S. MacNamara, "Kernel density estimation with linked boundary conditions," Studies in Applied Mathematics, 145(3), 357-396, 2020.
11. M. Colbrook, "Extending the unified transform: curvilinear polygons and variable coefficient PDEs," IMA Journal of Numerical Analysis, 40(2), 976-1004, 2020.
10. M. Colbrook, "Pseudoergodic operators and periodic boundary conditions," Mathematics of Computation, 89(322), 737-766, 2020.
9. M. Colbrook, M. Priddin, "Fast and spectrally accurate numerical methods for perforated screens," IMA Journal of Applied Mathematics, 85(5), 790-821, 2020.
8. M. Colbrook, B. Roman, A. Hansen, "How to compute spectra with error control," Physical Review Letters, 122(25), 250201, 2019. (cover article)
IMA Lighthill-Thwaites Prize 2021
Smith-Knight/Rayleigh-Knight Prize Class I 2018
Follow up article in IMA Mathematics Today: Unscrambling the Infinite: Can we Compute Spectra?
7. M. Colbrook, A. Hansen, "On the infinite-dimensional QR algorithm," Numerische Mathematik, 143(1), 17-83, 2019.
6. M. Colbrook, L. Ayton, A. Fokas, "The unified transform for mixed boundary condition problems in unbounded domains," Proceedings of the Royal Society A, 475(2222), 20180605, 2019.
IMA Lighthill-Thwaites Prize Finalist 2019
5. M. Colbrook, A. Fokas, P. Hashemzadeh, "A hybrid analytical-numerical technique for elliptic PDEs," SIAM Journal on Scientific Computing, 41(2), A1066-A1090, 2019.
4. M. Colbrook, L. Ayton, "A spectral collocation method for acoustic scattering by multiple elastic plates," Journal of Sound and Vibration, 461, 114904, 2019.
3. F. de Barros, M. Colbrook, A. Fokas, "A hybrid analytical-numerical method for solving advection-dispersion problems on a half-line," International Journal of Heat and Mass Transfer, 139, 482-491, 2019.
2. M. Colbrook, N. Flyer, B. Fornberg, "On the Fokas method for the solution of elliptic problems in both convex and non-convex polygonal domains," Journal of Computational Physics, 374, 996-1016, 2018.
1. M. Colbrook, X. Ma, P. Hopkins, J. Squire, "Scaling laws of passive-scalar diffusion in the interstellar medium," (my first paper and the outcome of my SURF scholarship at Caltech) Monthly Notices of the Royal Astronomical Society, 467(2), 2421-2429, 2017.


Published Conference Proceedings (chronological order)

6. H. Butt, S. Damani, S. Chaware, M. Szoke, S. Srivastava, T. Lowe, W. Devenport, A. Hales, M. Colbrook, L. Ayton, "Pressure Gradient Effects on Boundary Layer Superstructures," AIAA/CEAS Aeroacoustics, 2023, to appear.
5. M. Colbrook, A. Horning, "SpecSolve: Spectral methods for spectral measures," ICOSAHOM, 2022.
4. L. Ayton, M. Colbrook, T. Geyer, P. Chaitanya, E. Sarradj, "Modelling chordwise-varying porosity to reduce aerofoil-turbulence interaction noise," AIAA/CEAS Aeroacoustics, 2021.
3. M. Colbrook, L. Ayton, "Non-linear Forchheimer corrections in acoustic scattering," AIAA/CEAS Aeroacoustics, 2021.
2. M. Colbrook, V. Antun, A. Hansen, "On the existence of stable and accurate neural networks for image reconstruction," Signal Processing with Adaptive Sparse Structured Representations (SPARS), 2019.
1. L. Ayton, M. Colbrook, A. Fokas, "The unified transform: a spectral collocation method for acoustic scattering," AIAA/CEAS Aeroacoustics, 2019.


Submitted Articles

M. Colbrook "Another look at Residual Dynamic Mode Decomposition in the regime of fewer Snapshots than Dictionary Size" pdf
N. Boullé, M. Colbrook "On the Convergence of Hermitian Dynamic Mode Decomposition" arXiv
B. Adcock, M. Colbrook, M. Neyra-Nesterenko "Restarts subject to approximate sharpness: A parameter-free and optimal scheme for first-order methods" arXiv pdf
M. Colbrook, A. Townsend, "Avoiding discretization issues for nonlinear eigenvalue problems" arXiv
J. Ben-Artzi, M. Colbrook, A. Hansen, O. Nevanlinna, M. Seidel, "Computing Spectra - On the solvability complexity index hierarchy and towers of algorithms" arXiv pdf


Press Releases, Thesis, and Other Publications

SIAM News spotlight for SIAM Activity Group on Computational Science and Engineering Best Paper Prize. link
Notices of the AMS for SIAM Richard C. DiPrima Prize. link
SIAM News spotlight for SIAM Richard C. DiPrima Prize. link
"Some AI systems may be impossible to compute," Interview for IEEE spectrum, 2022. link
"Meet the JRF: Dr Matthew Colbrook explains how maths can help artificial intelligence," Interview for Trinity College, Cambridge, 2022. link
"Mathematical paradox demonstrates the limits of AI," Press Release, University of Cambridge Research News, 2022. link
M. Colbrook, "The Foundations of Infinite-Dimensional Spectral Computations," PhD thesis, University of Cambridge, 2020.
SIAM Richard C. DiPrima Prize 2022


Publication Profiles and Code

Google Scholar
Researchgate
Some of my code can be found on my GitHub profile.