67 citations · 177 across the 17 of their papers we have counts for
18 papers
Adversarial Training Without Input Gradients via Low-Rank Householder Expansions
Tiana C. Johnson, Donsub Rim
This work concerns adversarial training against the small-norm adversarial examples that arise from the inherent input instability of a trained deep neural network. Examples in thi…
Learning Low Rank Neural Representations of Hyperbolic Wave Dynamics from Data
Woojin Cho, Kookjin Lee, Noseong Park +2
We present a data-driven dimensionality reduction method that is well-suited for physics-based data representing hyperbolic wave propagation. The method utilizes a specialized neur…
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…
FastLRNR and Sparse Physics Informed Backpropagation
Woojin Cho, Kookjin Lee, Noseong Park +2
We introduce Sparse Physics Informed Backpropagation (SPInProp), a new class of methods for accelerating backpropagation for a specialized neural network architecture called Low Ra…
On the performance of sequential Bayesian update for database of diverse tsunami scenarios
Reika Nomura, Louise A. Hirao Vermare, Saneiki Fujita +4
Although the sequential tsunami scenario detection framework was validated in our previous work, several tasks remain to be resolved from a practical point of view. This study aims…
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…
Hypernetwork-based Meta-Learning for Low-Rank Physics-Informed Neural Networks
Woojin Cho, Kookjin Lee, Donsub Rim +1
In various engineering and applied science applications, repetitive numerical simulations of partial differential equations (PDEs) for varying input parameters are often required (…
A range characterization of the single-quadrant ADRT
Weilin Li, Kui Ren, Donsub Rim
This work characterizes the range of the single-quadrant approximate discrete Radon transform (ADRT) of square images. The characterization follows from a set of linear constraints…
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…
Model reduction of a parametrized scalar hyperbolic conservation law using displacement interpolation
Donsub Rim, Kyle T. Mandli
We propose a model reduction technique for parametrized partial differential equations arising from scalar hyperbolic conservation laws. The key idea of the technique is to constru…
Displacement interpolation using monotone rearrangement
Donsub Rim, Kyle T. Mandli
When approximating a function that depends on a parameter, one encounters many practical examples where linear interpolation or linear approximation with respect to the parameters…
Imaging of isotropic and anisotropic conductivities from power densities in three dimensions
François Monard, Donsub Rim
We present numerical reconstructions of anisotropic conductivity tensors in three dimensions, from knowledge of a finite family of power density functionals. Such a problem arises…
Dimensional splitting of hyperbolic partial differential equations using the Radon transform
Donsub Rim
We introduce a dimensional splitting method based on the intertwining property of the Radon transform, with a particular focus on its applications related to hyperbolic partial dif…
Transport reversal for model reduction of hyperbolic partial differential equations
Donsub Rim, Scott Moe, Randall J. LeVeque
Snapshot matrices built from solutions to hyperbolic partial differential equations exhibit slow decay in singular values, whereas fast decay is crucial for the success of projecti…
Generating Random Earthquake Events for PTHA
Randall J. LeVeque, Knut Waagan, Frank I. González +2
In order to perform probabilistic tsunami hazard assessment (PTHA) based on subduction zone earthquakes, it is necessary to start with a catalog of possible future events along wit…
An Elementary Proof That Symplectic Matrices Have Determinant One
Donsub Rim
We give one more proof of the fact that symplectic matrices over real and complex fields have determinant one. While this has already been proved many times, there has been lasting…