5 papers
Improving Learning of Green's Functions Through Kernel Decomposition
Beiji Chen, Qiang Du, Kui Ren +1
This work analyzes a framework for learning the solution operator, or equivalently, the Green's function, of a general self-adjoint second-order elliptic operator $\cL$. Subtractin…
Sampling Using Hybrid Stochastic Dynamics
Björn Engquist, Kui Ren, Yunan Yang
This work proposes a framework for sampling from the Gibbs distribution of a given potential using hybrid stochastic dynamics. In this framework, two distinct sampling dynamics are…
Recovering the initial condition and physical coefficients in a nonlinear PDE model of cell invasion
Beiji Chen, Kui Ren
This paper investigates an inverse problem for the simultaneous reconstruction of two spatially varying reaction coefficients, the local proliferation rate and the competition (sat…
A discontinuous Galerkin method for one-dimensional nonlocal wave problems
Qiang Du, Kui Ren, Lu Zhang +1
This paper presents a fully discrete numerical scheme for one-dimensional nonlocal wave equations and provides a rigorous theoretical analysis. To facilitate the spatial discretiza…
An energy-based discontinuous Galerkin method for the nonlinear Schrödinger equation with wave operator
Kui Ren, Lu Zhang, Yin Zhou
This work develops an energy-based discontinuous Galerkin (EDG) method for the nonlinear Schrödinger equation with the wave operator. The focus of the study is on the energy-conser…