11 citations · 15 across the 4 of their papers we have counts for
5 papers · 1 filter
An explicit spectral decomposition of the ADRT
Weilin Li, Karl Otness, Kui Ren +1
The approximate discrete Radon transform (ADRT) is a hierarchical multiscale approximation of the Radon transform. In this paper, we factor the ADRT into a product of linear transf…
A Low Rank Neural Representation of Entropy Solutions
Donsub Rim, Gerrit Welper
We construct a new representation of entropy solutions to nonlinear scalar conservation laws with a smooth convex flux function in a single spatial dimension. The representation is…
Depth separation for reduced deep networks in nonlinear model reduction: Distilling shock waves in nonlinear hyperbolic problems
Donsub Rim, Luca Venturi, Joan Bruna +1
Classical reduced models are low-rank approximations using a fixed basis designed to achieve dimensionality reduction of large-scale systems. In this work, we introduce reduced dee…
Manifold Approximations via Transported Subspaces: Model reduction for transport-dominated problems
Donsub Rim, Benjamin Peherstorfer, Kyle T. Mandli
This work presents a method for constructing online-efficient reduced models of large-scale systems governed by parametrized nonlinear scalar conservation laws. The solution manifo…
Exact and fast inversion of the approximate discrete Radon transform from partial data
Donsub Rim
We give an exact inversion formula for the approximate discrete Radon transform introduced in [Brady, SIAM J. Comput., 27(1), 107--119] that is of cost for a square 2…