About

I am an Assistant Professor at the Department of Mathematics in Washington University in St. Louis.

I will be on leave during the academic year 2024-2025 to be a Visiting Scholar at University of Washington.

I was a visiting assistant professor at the International Research Institute of Disaster Science (IRIDeS) in Tohoku University during the summer of 2023.

During years prior, I was at the Courant Institute and at Columbia University. I obtained my PhD at the University of Washington and my advisors were Randall J. LeVeque and Gunther Uhlmann.

[rim@wustl.edu] [CV: updated 2021/07/01].

Research Interests

My interests are in the numerical analysis of partial differential equations (PDEs) and inverse problems

• Real-time solutions to partial differential equations (PDEs) using Low Rank Neural Representations (LRNRs) with a focus on nonlinear systems of hyperbolic conservation laws
• Stability analysis of neural networks and their development in high-consequence applications in geophysics such as tsunami early warning
• Approximate discrete Radon transform (ADRT) and its applications: fast inversion, dimensional splitting, nonlinear dimensionality reduction, sparse approximations, neural networks
• Computational applications in geophysics, medical imaging, and plasma physics: real-time tsunami and storm surge prediction, coupled-physics imaging, and active control of plasma instabilities

Publications / Preprints / Software

An explicit spectral decomposition of the ADRT
W. Li, K. Otness, K. Ren, D. Rim
Preprint (2024) | [arXiv]

Identifying Contemporaneous and Lagged Dependence Structures by Promoting Sparsity in Continuous-time Neural Networks
F. Wu, W. Cho, D. Korotky, S. Hong, D. Rim, N. Park, K. Lee
CIKM24 (2024) | [doi]

FastLRNR and Sparse Physics Informed Backpropagation
W. Cho, K. Lee, N. Park, D. Rim, G. Welper
Results Appl Math 25 100547 (2025) | [doi][arXiv]

Comparative Performance of Scenario Superposition by Sequential Bayesian Update for Tsunami Risk Evaluation
R. Nomura, L. A. H. Vermare, S. Fujita, D. Rim, S. Moriguchi, R. J. LeVeque, K. Terada
J Disaster Res 19 (6) (2024) | [doi][arXiv]

A Low Rank Neural Representation of Entropy Solutions
D. Rim, G. Welper
Preprint (2024) | [arXiv]

Performance bounds for Reduced Order Models with Application to Parametric Transport
D. Rim, G. Welper
Preprint (2023) | [arXiv]

Hypernetwork-based Meta-Learning for Low-Rank Physics-Informed Neural Networks
W. Choi, K. Lee, D. Rim, N. Park
Adv Neural Inf Proc Sys (NeurIPS - spotlight) 36 11219-11231 (2023) | [doi][arXiv]

A Stability Analysis of Neural Networks and Its Application to Tsunami Early Warning
D. Rim, S. Suri, S. Hong, K. Lee, R. J. LeVeque
J Geophys Res: Machine Learning and Computation 1 e2024JH000223 (2024) | [doi][EarthArXiv]

adrt: approximate discrete Radon transform for Python
K. Otness, D. Rim
J Open Source Softw 8 (83) 5083 (2023) | [doi]

Tsunami Early Warning from Global Navigation Satellite System Data using Convolutional Neural Networks
D. Rim, R. Baraldi, C.M. Liu, R. J. LeVeque, K. Terada
Geophys Res Lett 49 e2022GL099511 (2022) | [doi][EarthArXiv]

A range characterization of the single-quadrant ADRT
W. Li, K. Ren, D. Rim
Math Comp 92 283-306 (2023) | [doi][arXiv]

Comparison of Machine Learning Approaches for Tsunami Forecasting from Sparse Observations
C.M. Liu, D. Rim, R. Baraldi, R. J. LeVeque
Pure Appl Geophys 178 5129-5153 (2021) | [doi][EarthArXiv]

A Source Clustering Approach for Efficient Inundation Modeling and Regional Scale PTHA
A. Williamson, D. Rim, L. Adams, R. J. LeVeque, D. Melgar, F. I. Gonzalez
Front Earth Sci 8:442 (2020) | [doi][EarthArXiv]

Depth separation for reduced deep networks in nonlinear model reduction: Distilling shock waves in nonlinear hyperbolic problems
D. Rim, L. Venturi, J. Bruna, B. Peherstorfer
Preprint (2020) | [arXiv]

Manifold Approximations via Transported Subspaces: Model reduction for transport-dominated problems
D. Rim, B. Peherstorfer, K. T. Mandli
SIAM J Sci Comput 45 (1) A170-A199 (2023) | [doi][arXiv]

Exact and fast inversion of the approximate discrete Radon transform from partial data
D. Rim
Appl Math Lett 102 106159 (2020) | [doi][arXiv]

The Effects of Earthquake Kinematics on Tsunami Propagation
A. Williamson, D. Melgar, D. Rim
J Geophys Res: Solid Earth 124 11639-11650 (2019) | [doi]

Model reduction of a parametrized scalar hyperbolic conservation law using displacement interpolation
D. Rim and K. T. Mandli
Preprint (2018) | [arXiv][github]

Dimensional splitting of hyperbolic partial differential equations using the Radon transform
D. Rim
SIAM J Sci Comput 40 (6) A4184–A4207 (2018) | [doi][arXiv]

Displacement interpolation using monotone rearrangement
D. Rim and K. T. Mandli
SIAM/ASA J Uncertainty Quantification 6 (4), 1503-1531 (2018) | [doi][arXiv][github]

Imaging of isotropic and anisotropic conductivities from power densities in three dimensions
F. Monard and D. Rim
Inverse Probl 34 (7) 075005 (2018) | [doi][arXiv][github]

Transport reversal for model reduction of hyperbolic partial differential equations
D. Rim, S. Moe, and R. J. LeVeque
SIAM/ASA J Uncertainty Quantification 6 (1) 118-150 (2018) | [doi][arXiv]

An elementary proof that symplectic matrices have determinant one
D. Rim
Adv Dyn Syst Appl 12 (1) 15-20 (2017) | [doi][arXiv]

Generating random earthquake events for probabilistic tsunami hazard assessment (PTHA)
R. J. LeVeque, K. Waagan, F. I. Gonzalez, D. Rim, and G. Lin
Pure Appl Geophys 173: 3671 (2016) | [doi][arXiv]

Explicit error estimates for Courant, Crouzeix-Raviart and Raviart-Thomas finite element methods
C. Carstensen, J. Gedicke, and D. Rim
J Comput Math 30 no. 4 337-353 (2012) | [doi][Preprint]

More Numerical Software

For a full list of relevant numerical softwares, please visit my github page.
See also: Top ten reasons to not share your code (and why you should anyway).

People