47 citations · 317 across the 48 of their papers we have counts for
10 papers · 1 filter
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…