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 (accepted) (2024) | [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
- Loyce M. Adams
- Jacob Blum
- Joan Bruna
- Carsten Carstensen
- Woojin Cho
- Minseok Choi
- Swarup Dhar
- Qiang Du
- Sanghyun Hong
- Tiana Johnson
- Joscha Gedicke
- Frank I. Gonzalez
- Kookjin Lee
- Weilin Li
- Randall J. LeVeque
- Guang Lin
- Kyle T. Mandli
- Diego Melgar
- Scott Moe
- Francois Monard
- Shuji Moriguchi
- Reika Nomura
- Karl Otness
- Noseong Park
- Kui Ren
- Victor Song
- Sanah Suri
- Kenjiro Terada
- Gunther Uhlmann
- Karsten Urban
- Luca Venturi
- Knut Waagan
- Gerrit Welper
- Amy Williamson