196 citations · 1.6k across the 143 of their papers we have counts for
24 papers · 1 filter
Numerical methods for stochastic differential equations based on Gaussian mixture
Lei Li, Jianfeng Lu, Jonathan Mattingly +1
We develop in this work a numerical method for stochastic differential equations (SDEs) with weak second order accuracy based on Gaussian mixture. Unlike the conventional higher or…
On Pointwise Products of Elliptic Eigenfunctions
Jianfeng Lu, Stefan Steinerberger
We consider eigenfunctions of Schrödinger operators on a dimensional bounded domain (or a dimensional compact manifold ) with Dirichlet conditions. These operators g…
Approximating Pointwise Products of Laplacian Eigenfunctions
Jianfeng Lu, Christopher D. Sogge, Stefan Steinerberger
We consider Laplacian eigenfunctions on a dimensional bounded domain (or a dimensional compact manifold ) with Dirichlet conditions. These operators give rise to a s…
Continuum limit and preconditioned Langevin sampling of the path integral molecular dynamics
Jianfeng Lu, Yulong Lu, Zhennan Zhou
We investigate the continuum limit that the number of beads goes to infinity in the ring polymer representation of thermal averages. Studying the continuum limit of the trajectory…
Inchworm Monte Carlo method for open quantum systems
Zhenning Cai, Jianfeng Lu, Siyao Yang
We investigate in this work a recently proposed diagrammatic quantum Monte Carlo method --- the inchworm Monte Carlo method --- for open quantum systems. We establish its validity…
A Numerical method for coupling the BGK model and Euler equation through the linearized Knudsen layer
Hongxu Chen, Qin Li, Jianfeng Lu
The Bhatnagar-Gross-Krook (BGK) model, a simplification of the Boltzmann equation, in the absence of boundary effect, converges to the Euler equations when the Knudsen number is sm…
Computing edge states without hard truncation
Kyle Thicke, Alexander B. Watson, Jianfeng Lu
We present a numerical method which accurately computes the discrete spectrum and associated bound states of Hamiltonians which model electronic "edge" states localized at boundari…
Gradient flow structure and exponential decay of the sandwiched Rényi divergence for primitive Lindblad equations with GNS-detailed balance
Yu Cao, Jianfeng Lu, Yulong Lu
We study the entropy production of the sandwiched Rényi divergence under the primitive Lindblad equation with GNS-detailed balance. We prove that the Lindblad equation can be ident…
Simulated Tempering Method in the Infinite Switch Limit with Adaptive Weight Learning
Anton Martinsson, Jianfeng Lu, Benedict Leimkuhler +1
We investigate the theoretical foundations of the simulated tempering method and use our findings to design efficient algorithms. Employing a large deviation argument first used fo…
Dirac operators and domain walls
Jianfeng Lu, Alexander B. Watson, Michael I. Weinstein
We study the eigenvalue problem for a one-dimensional Dirac operator with a spatially varying ``mass'' term. It is well-known that when the mass function has the form of a kink, or…
Random Sampling and Efficient Algorithms for Multiscale PDEs
Ke Chen, Qin Li, Jianfeng Lu +1
We describe a numerical framework that uses random sampling to efficiently capture low-rank local solution spaces of multiscale PDE problems arising in domain decomposition. In con…
Integrated Tempering Enhanced Sampling Method as the Infinite Switching Limit of Simulated Tempering
Zhiyi You, Liying Li, Jianfeng Lu +1
Fast and accurate sampling method is in high demand, in order to bridge the large gaps between molecular dynamic simulations and experimental observations. Recently, integrated tem…
Coordinate-wise descent methods for leading eigenvalue problem
Yingzhou Li, Jianfeng Lu, Zhe Wang
Leading eigenvalue problems for large scale matrices arise in many applications. Coordinate-wise descent methods are considered in this work for such problems based on a reformulat…
Stochastic modified equations for the asynchronous stochastic gradient descent
Jing An, Jianfeng Lu, Lexing Ying
We propose a stochastic modified equations (SME) for modeling the asynchronous stochastic gradient descent (ASGD) algorithms. The resulting SME of Langevin type extracts more infor…
Exponential decay of Rényi divergence under Fokker-Planck equations
Yu Cao, Jianfeng Lu, Yulong Lu
We prove the exponential convergence to the equilibrium, quantified by Rényi divergence, of the solution of the Fokker-Planck equation with drift given by the gradient of a strictl…
Scaling limit of the Stein variational gradient descent: the mean field regime
Jianfeng Lu, Yulong Lu, James Nolen
We study an interacting particle system in motivated by Stein variational gradient descent [Q. Liu and D. Wang, NIPS 2016], a deterministic algorithm for sampling fr…
Quadrature Points via Heat Kernel Repulsion
Jianfeng Lu, Matthias Sachs, Stefan Steinerberger
We discuss the classical problem of how to pick weighted points on a dimensional manifold so as to obtain a reasonable quadrature rule $$ \frac{1}{|M|}\int_{M}{f(x) dx} \si…
Optimal artificial boundary condition for random elliptic media
Jianfeng Lu, Felix Otto
We are given a uniformly elliptic coefficient field that we regard as a realization of a stationary and finite-range (say, range unity) ensemble of coefficient fields. Given a (det…
On discrete Wigner transforms
Zhenning Cai, Jianfeng Lu, Kevin Stubbs
In this work, we derive a discrete analog of the Wigner transform over the space for any prime and any positive integer . We show that the Wigne…
Stochastic dynamical low-rank approximation method
Yu Cao, Jianfeng Lu
In this paper, we extend the dynamical low-rank approximation method to the space of finite signed measures. Under this framework, we derive stochastic low-rank dynamics for stocha…
Solving for high dimensional committor functions using artificial neural networks
Yuehaw Khoo, Jianfeng Lu, Lexing Ying
In this note we propose a method based on artificial neural network to study the transition between states governed by stochastic processes. In particular, we aim for numerical sch…
Fundamental limitations for measurements in quantum many-body systems
Thomas Barthel, Jianfeng Lu
Dynamical measurement schemes are an important tool for the investigation of quantum many-body systems, especially in the age of quantum simulation. Here, we address the question w…
Learning interacting particle systems: diffusion parameter estimation for aggregation equations
Hui Huang, Jian-Guo Liu, Jianfeng Lu
In this article, we study the parameter estimation of interacting particle systems subject to the Newtonian aggregation and Brownian diffusion. Specifically, we construct an estima…
Randomized sampling for basis functions construction in generalized finite element methods
Ke Chen, Qin Li, Jianfeng Lu +1
In the framework of generalized finite element methods for elliptic equations with rough coefficients, efficiency and accuracy of the numerical method depend critically on the use…