47 citations · 317 across the 48 of their papers we have counts for
50 papers
Beyond expectations: Residual Dynamic Mode Decomposition and Variance for Stochastic Dynamical Systems
Matthew J. Colbrook, Qin Li, Ryan V. Raut +1
Koopman operators linearize nonlinear dynamical systems, making their spectral information of crucial interest. Numerous algorithms have been developed to approximate these spectra…
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…
Computation of optimal beams in weak turbulence
Qin Li, Anjali Nair, Samuel N Stechmann
When an optical beam propagates through a turbulent medium such as the atmosphere or ocean, the beam will become distorted. It is then natural to seek the best or optimal beam that…
Second-order diffusion limit for the phonon transport equation-asymptotics and numerics
Anjali Nair, Qin Li, Weiran Sun
We investigate the numerical implementation of the limiting equation for the phonon transport equation in the small Knudsen number regime. The main contribution is that we derive t…
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…
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…
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…
Random Coordinate Underdamped Langevin Monte Carlo
Zhiyan Ding, Qin Li, Jianfeng Lu +1
The Underdamped Langevin Monte Carlo (ULMC) is a popular Markov chain Monte Carlo sampling method. It requires the computation of the full gradient of the log-density at each itera…
Random Coordinate Langevin Monte Carlo
Zhiyan Ding, Qin Li, Jianfeng Lu +1
Langevin Monte Carlo (LMC) is a popular Markov chain Monte Carlo sampling method. One drawback is that it requires the computation of the full gradient at each iteration, an expens…
Langevin Monte Carlo: random coordinate descent and variance reduction
Zhiyan Ding, Qin Li
Langevin Monte Carlo (LMC) is a popular Bayesian sampling method. For the log-concave distribution function, the method converges exponentially fast, up to a controllable discretiz…
Reconstruction of the emission coefficient in the nonlinear radiative transfer equation
Christian Klingenberg, Ru-Yu Lai, Qin Li
In this paper, we investigate an inverse problem for the radiative transfer equation that is coupled with a heat equation in a nonscattering medium in , . Th…
Variance reduction for Random Coordinate Descent-Langevin Monte Carlo
Zhiyan Ding, Qin Li
Sampling from a log-concave distribution function is one core problem that has wide applications in Bayesian statistics and machine learning. While most gradient free methods have…
Ensemble Kalman Inversion for nonlinear problems: weights, consistency, and variance bounds
Zhiyan Ding, Qin Li, Jianfeng Lu
Ensemble Kalman Inversion (EnKI) and Ensemble Square Root Filter (EnSRF) are popular sampling methods for obtaining a target posterior distribution. They can be seem as one step (t…
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…
On diffusive scaling in acousto-optic imaging
Francis J. Chung, Ru-Yu Lai, Qin Li
Acousto-optic imaging (AOI) is a hybrid imaging process. By perturbing the to-be-reconstructed tissues with acoustic waves, one introduces the interaction between the acoustic and…
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…