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08/21/2023
Beyond expectations: Residual Dynamic Mode Decomposition and Variance for Stochastic Dynamical Systems
Koopman operators linearize nonlinear dynamical systems, making their sp...
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05/02/2023
Avoiding discretization issues for nonlinear eigenvalue problems
The first step when solving an infinite-dimensional eigenvalue problem i...
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04/07/2023
Leveraging the Hankel norm approximation and block-AAA algorithms in reduced order modeling
Large-scale linear, time-invariant (LTI) dynamical systems are widely us...
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02/24/2023
Elliptic PDE learning is provably data-efficient
PDE learning is an emerging field that combines physics and machine lear...
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02/14/2023
Are sketch-and-precondition least squares solvers numerically stable?
Sketch-and-precondition techniques are popular for solving large least s...
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12/19/2022
Matrix recovery from matrix-vector products
Can one recover a matrix efficiently from only matrix-vector products? I...
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10/13/2022
Probabilistic Missing Value Imputation for Mixed Categorical and Ordered Data
Many real-world datasets contain missing entries and mixed data types in...
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05/28/2022
A Quadrature Perspective on Frequency Bias in Neural Network Training with Nonuniform Data
Small generalization errors of over-parameterized neural networks (NNs) ...
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04/27/2022
Learning Green's functions associated with parabolic partial differential equations
Given input-output pairs from a parabolic partial differential equation ...
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02/09/2022
On the stability of unevenly spaced samples for interpolation and quadrature
Unevenly spaced samples from a periodic function are common in signal pr...
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11/29/2021
Rigorous data-driven computation of spectral properties of Koopman operators for dynamical systems
Koopman operators are infinite-dimensional operators that globally linea...
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11/19/2021
Parallel algorithms for computing the tensor-train decomposition
The tensor-train (TT) decomposition expresses a tensor in a data-sparse ...
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09/23/2021
Arbitrary-Depth Universal Approximation Theorems for Operator Neural Networks
The standard Universal Approximation Theorem for operator neural network...
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05/27/2021
A generalization of the randomized singular value decomposition
The randomized singular value decomposition (SVD) is a popular and effec...
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05/16/2021
Data-driven Algorithms for signal processing with rational functions
Rational approximation schemes for reconstructing signals from samples w...
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05/01/2021
Data-driven discovery of physical laws with human-understandable deep learning
There is an opportunity for deep learning to revolutionize science and t...
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03/30/2021
An optimal complexity spectral method for Navier–Stokes simulations in the ball
We develop a spectral method for solving the incompressible generalized ...
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01/31/2021
Learning elliptic partial differential equations with randomized linear algebra
Given input-output pairs of an elliptic partial differential equation (P...
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10/29/2020
Over-parametrized neural networks as under-determined linear systems
We draw connections between simple neural networks and under-determined ...
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06/15/2020
The ultraspherical spectral element method
We introduce a novel spectral element method based on the ultraspherical...
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06/02/2020
Computing spectral measures of self-adjoint operators
Using the resolvent operator, we develop an algorithm for computing smoo...
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04/04/2020
Rational neural networks
We consider neural networks with rational activation functions. The choi...
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02/10/2020
Anderson Acceleration Using the H^-s Norm
Anderson acceleration (AA) is a technique for accelerating the convergen...
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11/26/2019
Bounding Zolotarev numbers using Faber rational functions
By closely following a construction by Ganelius, we construct Faber rati...
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10/31/2019
Computing with functions in the ball
A collection of algorithms in object-oriented MATLAB is described for nu...
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09/22/2018
Chebyshev approximation and the global geometry of sloppy models
Sloppy models are complex nonlinear models with outcomes that are signif...
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05/21/2017