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

• Nonlinear model reduction methods using Low Rank Neural Representations (LRNRs) for parametrized nonlinear systems of hyperbolic conservation laws
• Approximate discrete Radon transform (ADRT) and its applications: fast inversion, dimensional splitting, nonlinear dimensionality reduction, sparse approximations
• 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

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
Proceedings of the 33rd ACM International Conference on Knowledge Management (2024) | [doi]

FastLRNR and Sparse Physics Informed Backpropagation
W. Cho, K. Lee, N. Park, D. Rim, G. Welper
Preprint (2024) | [arXiv]

On the performance of sequential Bayesian update for database of diverse tsunami scenarios
R. Nomura, L. A. H. Vermare, S. Fujita, D. Rim, S. Moriguchi, R. J. LeVeque, K. Terada
Journal of Disaster Research 19 (6) (2024) | [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
Advances in Neural Information Processing Systems 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
Journal of Geophysical Research: Machine Learning and Computation, accepted (2023) | [EarthArXiv]

adrt: approximate discrete Radon transform for Python
K. Otness, D. Rim
Journal of Open Source Software 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
Geophysical Research Letters 49 e2022GL099511 (2022) | [doi][EarthArXiv]

A range characterization of the single-quadrant ADRT
W. Li, K. Ren, D. Rim
Mathematics of Computation 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 and Applied Geophysics 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
Frontiers of Earth Science 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 Journal of Scientific Computing 45 (1) A170-A199 (2023) | [doi][arXiv]

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

The Effects of Earthquake Kinematics on Tsunami Propagation
A. Williamson, D. Melgar, D. Rim
Journal of Geophysical Research: 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 Journal of Scientific Computing 40 (6) A4184–A4207 (2018) | [doi][arXiv]

Displacement interpolation using monotone rearrangement
D. Rim and K. T. Mandli
SIAM/ASA Journal of 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 Problems 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 Journal of Uncertainty Quantification 6 (1) 118-150 (2018) | [doi][arXiv]

An elementary proof that symplectic matrices have determinant one
D. Rim
Advances in Dynamical Systems and Applications 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 and Applied Geophysics 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
Journal of Computational Mathematics 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