47 citations · 317 across the 48 of their papers we have counts for
8 papers · 1 filter
On the Global Convergence of Gradient Descent for multi-layer ResNets in the mean-field regime
Zhiyan Ding, Shi Chen, Qin Li +1
Finding the optimal configuration of parameters in ResNet is a nonconvex minimization problem, but first-order methods nevertheless find the global optimum in the overparameterized…
Low-rank approximation for multiscale PDEs
Ke Chen, Shi Chen, Qin Li +2
Historically, analysis for multiscale PDEs is largely unified while numerical schemes tend to be equation-specific. In this paper, we propose a unified framework for computing mult…
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…
Multiscale convergence of the inverse problem for chemotaxis in the Bayesian setting
Kathrin Hellmuth, Christian Klingenberg, Qin Li +1
Chemotaxis describes the movement of an organism, such as single or multi-cellular organisms and bacteria, in response to a chemical stimulus. Two widely used models to describe th…
Bridging and Improving Theoretical and Computational Electric Impedance Tomography via Data Completion
Tan Bui-Thanh, Qin Li, Leonardo Zepeda-Núñez
In computational PDE-based inverse problems, a finite amount of data is collected to infer unknown parameters in the PDE. In order to obtain accurate inferences, the collected data…
Overparameterization of deep ResNet: zero loss and mean-field analysis
Zhiyan Ding, Shi Chen, Qin Li +1
Finding parameters in a deep neural network (NN) that fit training data is a nonconvex optimization problem, but a basic first-order optimization method (gradient descent) finds a…
Local Well-posedness of Vlasov-Poisson-Boltzmann Equation with Generalized Diffuse Boundary Condition
Hongxu Chen, Chanwoo Kim, Qin Li
The Vlasov-Poisson-Boltzmann equation is a classical equation governing the dynamics of charged particles with the electric force being self-imposed. We consider the system in a co…
Constrained Ensemble Langevin Monte Carlo
Zhiyan Ding, Qin Li
The classical Langevin Monte Carlo method looks for samples from a target distribution by descending the samples along the gradient of the target distribution. The method enjoys a…