3 citations · 8 across the 12 of their papers we have counts for
13 papers
A Good Score Does not Lead to A Good Generative Model
Sixu Li, Shi Chen, Qin Li
Score-based Generative Models (SGMs) is one leading method in generative modeling, renowned for their ability to generate high-quality samples from complex, high-dimensional data d…
Bayesian sampling using interacting particles
Shi Chen, Zhiyan Ding, Qin Li
Bayesian sampling is an important task in statistics and machine learning. Over the past decade, many ensemble-type sampling methods have been proposed. In contrast to the classica…
Accelerating optimization over the space of probability measures
Shi Chen, Qin Li, Oliver Tse +1
The acceleration of gradient-based optimization methods is a subject of significant practical and theoretical importance, particularly within machine learning applications. While m…
Correcting Auto-Differentiation in Neural-ODE Training
Yewei Xu, Shi Chen, Qin Li
Does the use of auto-differentiation yield reasonable updates for deep neural networks (DNNs)? Specifically, when DNNs are designed to adhere to neural ODE architectures, can we tr…
On optimal bases for multiscale PDEs and Bayesian homogenization
Shi Chen, Zhiyan Ding, Qin Li +1
PDE solutions are numerically represented by basis functions. Classical methods employ pre-defined bases that encode minimum desired PDE properties, which naturally cause redundant…
High-frequency limit of the inverse scattering problem: asymptotic convergence from inverse Helmholtz to inverse Liouville
Shi Chen, Zhiyan Ding, Qin Li +1
We investigate the asymptotic relation between the inverse problems relying on the Helmholtz equation and the radiative transfer equation (RTE) as physical models, in the high-freq…
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…
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…
Semi-classical limit of an inverse problem for the Schrödinger equation
Shi Chen, Qin Li
It is a classical derivation that the Wigner equation, derived from the Schrödinger equation that contains the quantum information, converges to the Liouville equation when the res…
Manifold Learning and Nonlinear Homogenization
Shi Chen, Qin Li, Jianfeng Lu +1
We describe an efficient domain decomposition-based framework for nonlinear multiscale PDE problems. The framework is inspired by manifold learning techniques and exploits the tang…
Classical limit for the varying-mass Schrödinger equation with random inhomogeneities
Shi Chen, Qin Li, Xu Yang
The varying-mass Schrödinger equation (VMSE) has been successfully applied to model electronic properties of semiconductor hetero-structures, for example, quantum dots and quantum…