19 citations · 26 across the 11 of their papers we have counts for
13 papers
A Complete Resolution of Forsythe's Conjecture for Restarted Conjugate Gradients
Matthew J. Colbrook, George Stepaniants, Alex Townsend
Forsythe's conjecture, published in 1968, asserts that for each restart length , every exact-arithmetic restarted conjugate-gradient iteration on a real symmetric positive defin…
A computer-assisted counterexample to the planar Berenstein conjecture
Matthew J. Colbrook, Siavash Sadeghi, George Stepaniants
Recent work of Colbrook and Stepaniants produced the first counterexamples to the planar Pompeiu and Schiffer conjectures and introduced the conformal fixed-disc, disk-polynomial,…
A Proof of the Forsythe Conjecture for the Two-Step Restarted Conjugate Gradient Method
Matthew J. Colbrook, George Stepaniants, Alex Townsend
Forsythe conjectured in 1968 that the normalized residual directions of restarted conjugate gradients approach a two-cycle. We prove the conjecture for restart length two: unless t…
A computer-assisted counterexample to the planar Pompeiu and Schiffer conjectures
Matthew J. Colbrook, George Stepaniants
The planar Pompeiu problem, originating in 1929, and the associated Schiffer conjecture are long-standing rigidity questions linking rigid-motion integral transforms and Fourier ze…
A Spectral Theory of Scalar Volterra Equations
David Darrow, George Stepaniants
This work aims to bridge the gap between pure and applied research on scalar, linear Volterra equations by examining five major classes: integral and integro-differential equations…
Learning Memory and Material Dependent Constitutive Laws
Kaushik Bhattacharya, Lianghao Cao, George Stepaniants +2
We propose and study a neural operator framework for learning memory- and material microstructure-dependent constitutive laws for heterogeneous materials. We work in the two-scale…
Covariance alignment: from maximum likelihood estimation to Gromov-Wasserstein
Yanjun Han, Philippe Rigollet, George Stepaniants
Feature alignment methods are used in many scientific disciplines for data pooling, annotation, and comparison. As an instance of a permutation learning problem, feature alignment…
Optimal transport for automatic alignment of untargeted metabolomic data
Marie Breeur, George Stepaniants, Pekka Keski-Rahkonen +2
Untargeted metabolomic profiling through liquid chromatography-mass spectrometry (LC-MS) measures a vast array of metabolites within biospecimens, advancing drug development, disea…
Discovering dynamics and parameters of nonlinear oscillatory and chaotic systems from partial observations
George Stepaniants, Alasdair D. Hastewell, Dominic J. Skinner +2
Despite rapid progress in live-imaging techniques, many complex biophysical and biochemical systems remain only partially observable, thus posing the challenge to identify valid th…
GULP: a prediction-based metric between representations
Enric Boix-Adsera, Hannah Lawrence, George Stepaniants +1
Comparing the representations learned by different neural networks has recently emerged as a key tool to understand various architectures and ultimately optimize them. In this work…
Learning Partial Differential Equations in Reproducing Kernel Hilbert Spaces
George Stepaniants
We propose a new data-driven approach for learning the fundamental solutions (Green's functions) of various linear partial differential equations (PDEs) given sample pairs of input…
Fast and Smooth Interpolation on Wasserstein Space
Sinho Chewi, Julien Clancy, Thibaut Le Gouic +3
We propose a new method for smoothly interpolating probability measures using the geometry of optimal transport. To that end, we reduce this problem to the classical Euclidean sett…
Inferring Causal Networks of Dynamical Systems through Transient Dynamics and Perturbation
George Stepaniants, Bingni W. Brunton, J. Nathan Kutz
Inferring causal relations from time series measurements is an ill-posed mathematical problem, where typically an infinite number of potential solutions can reproduce the given dat…