47 citations · 317 across the 48 of their papers we have counts for
8 papers · 1 filter
Error Lower Bounds of Constant Step-size Stochastic Gradient Descent
Zhiyan Ding, Yiding Chen, Qin Li +1
Stochastic Gradient Descent (SGD) plays a central role in modern machine learning. While there is extensive work on providing error upper bound for SGD, not much is known about SGD…
Schwarz iteration method for elliptic equation with rough media based on random sampling
Ke Chen, Qin Li, Stephen J. Wright
We propose a computationally efficient Schwarz method for elliptic equations with rough media. A random sampling strategy is used to find low-rank approximations of all local solut…
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…
Ensemble Kalman Inversion: mean-field limit and convergence analysis
Zhiyan Ding, Qin Li
Ensemble Kalman Inversion (EKI) has been a very popular algorithm used in Bayesian inverse problems. It samples particles from a prior distribution, and introduces a motion to move…
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…
A low-rank Schwarz method for radiative transport equation with heterogeneous scattering coefficient
Ke Chen, Qin Li, Jianfeng Lu +1
Random sampling has been used to find low-rank structure and to build fast direct solvers for multiscale partial differential equations of various types. In this work, we design an…
Parameter Reconstruction for general transport equation
Ru-Yu Lai, Qin Li
We consider the inverse problem for the general transport equation with external field, source term and absorption coefficient. We show that the source and the absorption coefficie…
Generalized multiscale finite element method for the steady state linear Boltzmann equation
Eric Chung, Yalchin Efendiev, Yanbo Li +1
The Boltzmann equation, as a model equation in statistical mechanics, is used to describe the statistical behavior of a large number of particles driven by the same physics laws. D…