73 citations · 398 across the 44 of their papers we have counts for
9 papers · 1 filter
Parallel algorithms for computing the tensor-train decomposition
Tianyi Shi, Maximilian Ruth, Alex Townsend
The tensor-train (TT) decomposition expresses a tensor in a data-sparse format used in molecular simulations, high-order correlation functions, and optimization. In this paper, we…
Rigorous data-driven computation of spectral properties of Koopman operators for dynamical systems
Matthew J. Colbrook, Alex Townsend
Koopman operators are infinite-dimensional operators that globally linearize nonlinear dynamical systems, making their spectral information valuable for understanding dynamics. How…
Arbitrary-Depth Universal Approximation Theorems for Operator Neural Networks
Annan Yu, Chloé Becquey, Diana Halikias +2
The standard Universal Approximation Theorem for operator neural networks (NNs) holds for arbitrary width and bounded depth. Here, we prove that operator NNs of bounded width and a…
Sufficiently dense Kuramoto networks are globally synchronizing
Martin Kassabov, Steven H. Strogatz, Alex Townsend
Consider any network of identical Kuramoto oscillators in which each oscillator is coupled bidirectionally with unit strength to at least other oscillators. There is a…
A generalization of the randomized singular value decomposition
Nicolas Boullé, Alex Townsend
The randomized singular value decomposition (SVD) is a popular and effective algorithm for computing a near-best rank approximation of a matrix using matrix-vector products…
Data-driven Algorithms for signal processing with trigonometric rational functions
Heather Wilber, Anil Damle, Alex Townsend
Rational approximation schemes for reconstructing periodic signals from samples with poorly separated spectral content are described. These methods are automatic and adaptive, requ…