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- University of Wisconsin–MadisonUS38 papers
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6 papers · 1 filter
A reduced order Schwarz method for nonlinear multiscale elliptic equations based on two-layer neural networks
Shi Chen, Zhiyan Ding, Qin Li +1
Neural networks are powerful tools for approximating high dimensional data that have been used in many contexts, including solution of partial differential equations (PDEs). We des…
Ensemble Kalman Sampler: mean-field limit and convergence analysis
Zhiyan Ding, Qin Li
Ensemble Kalman Sampler (EKS) is a method to find approximately samples from a target distribution. As of today, why the algorithm works and how it converges is mostly unk…
Dynamical low-rank integrator for the linear Boltzmann equation: error analysis in the diffusion limit
Zhiyan Ding, Lukas Einkemmer, Qin Li
Dynamical low-rank algorithms are a class of numerical methods that compute low-rank approximations of dynamical systems. This is accomplished by projecting the dynamics onto a low…
Survey of multifidelity methods in uncertainty propagation, inference, and optimization
Benjamin Peherstorfer, Karen Willcox, Max Gunzburger
In many situations across computational science and engineering, multiple computational models are available that describe a system of interest. These different models have varying…
Stability of inverse transport equation in diffusion scaling and Fokker-Planck limit
Ke Chen, Qin Li, Li Wang
We consider the inverse problem of reconstructing the scattering and absorption coefficients using boundary measurements for a time dependent radiative transfer equation (RTE). As…
Implicit Asymptotic Preserving Method for Linear Transport Equations
Qin Li, Li Wang
The computation of the radiative transfer equation is expensive mainly due to two stiff terms: the transport term and the collision operator. The stiffness in the former comes from…