8 citations · 19 across the 10 of their papers we have counts for
10 papers
Second-order consistency for learning chaotic dynamics via randomized Jacobian matching
Shinhoo Kang, Hai V. Nguyen, Tan Bui-Thanh
Short-horizon accuracy does not ensure that a learned chaotic system has correct long-time dynamics. Trajectory (zeroth-order) matching constrains vector-field values, and Jacobian…
Differentiable DG with Neural Operator Source Term Correction
Shinhoo Kang, Emil M. Constantinescu
Computational advances have fundamentally transformed the landscape of numerical simulations, enabling unprecedented levels of complexity and precision in modeling physical phenome…
Unified -HDG Frameworks for Friedrichs' PDE systems
Jau-Uei Chen, Shinhoo Kang, Tan Bui-Thanh +1
This work proposes a unified -adaptivity framework for hybridized discontinuous Galerkin (HDG) method for a large class of partial differential equations (PDEs) of Friedrichs'…
Learning Subgrid-scale Models with Neural Ordinary Differential Equations
Shinhoo Kang, Emil M. Constantinescu
We propose a new approach to learning the subgrid-scale model when simulating partial differential equations (PDEs) solved by the method of lines and their representation in chaoti…
Multirate Partitioned Runge-Kutta Methods for Coupled Navier-Stokes Equations
Shinhoo Kang, Alp Dener, Aidan Hamilton +3
Earth system models are complex integrated models of atmosphere, ocean, sea ice, and land surface. Coupling the components can be a significant challenge due to the difference in p…
Entropy-Preserving and Entropy-Stable Relaxation IMEX and Multirate Time-Stepping Methods
Shinhoo Kang, Emil M. Constantinescu
We propose entropy-preserving and entropy-stable partitioned Runge--Kutta (RK) methods. In particular, we extend the explicit relaxation Runge--Kutta methods to IMEX--RK methods an…
Mass-Conserving Implicit-Explicit Methods for Coupled Compressible Navier-Stokes Equations
Shinhoo Kang, Emil M. Constantinescu, Hong Zhang +1
Earth system models are composed of coupled components that separately model systems such as the global atmosphere, ocean, and land surface. While these components are well develop…
A scalable exponential-DG approach for nonlinear conservation laws: with application to Burger and Euler equations
Shinhoo Kang, Tan Bui-Thanh
We propose an Exponential DG approach for numerically solving partial differential equations (PDEs). The idea is to decompose the governing PDE operators into linear (fast dynamics…
A Hybridized Discontinuous Galerkin Method for A Linear Degenerate Elliptic Equation Arising from Two-Phase Mixtures
Shinhoo Kang, Tan Bui-Thanh, Todd Arbogast
We develop a high-order hybridized discontinuous Galerkin (HDG) method for a linear degenerate elliptic equation arising from a two-phase mixture of mantle convection or glacier dy…
IMEX HDG-DG: a coupled implicit hybridized discontinuous Galerkin (HDG) and explicit discontinuous Galerkin (DG) approach for shallow water systems
Shinhoo Kang, Francis X. Giraldo, Tan Bui-Thanh
We propose IMEX HDG-DG schemes for planar and spherical shallow water systems. Of interest is subcritical flow, where the speed of the gravity wave is faster than that of nonlinear…