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20162026
most citedCan stable and accurate neural networks be computed? -- On the barriers of deep learning and Smale's 18th problem

130 citations · 345 across the 38 of their papers we have counts for

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Showing 2022Show all

3 papers · 1 filter

math.NA2022★ 1 cited

The mpEDMD Algorithm for Data-Driven Computations of Measure-Preserving Dynamical Systems

Matthew J. Colbrook

Koopman operators globally linearize nonlinear dynamical systems and their spectral information is a powerful tool for the analysis and decomposition of nonlinear dynamical systems…

physics.flu-dyn2022★ 88 cited

Residual Dynamic Mode Decomposition: Robust and verified Koopmanism

Matthew J. Colbrook, Lorna J. Ayton, Máté Szőke

Dynamic Mode Decomposition (DMD) describes complex dynamic processes through a hierarchy of simpler coherent features. DMD is regularly used to understand the fundamental character…

math.NA2022

SpecSolve: Spectral methods for spectral measures

Matthew J. Colbrook, Andrew Horning

Self-adjoint operators on infinite-dimensional spaces with continuous spectra are abundant but do not possess a basis of eigenfunctions. Rather, diagonalization is achieved through…