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Browsing by Author "Lu, Jianfeng"
Now showing items 1-20 of 28
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A Hybrid Global-local Numerical Method for Multiscale PDEs
(2017-04-23)We present a new hybrid numerical method for multiscale partial differential equations, which simultaneously captures both the global macroscopic information and resolves the local microscopic events. The convergence of ... -
A Priori Generalization Analysis of the Deep Ritz Method for Solving High Dimensional Elliptic Equations
This paper concerns the a priori generalization analysis of the Deep Ritz Method (DRM) [W. E and B. Yu, 2017], a popular neural-network-based method for solving high dimensional partial differential equations. We derive ... -
A Variation on the Donsker-Varadhan Inequality for the Principial Eigenvalue
(2017-04-23)The purpose of this short note is to give a variation on the classical Donsker-Varadhan inequality, which bounds the first eigenvalue of a second-order elliptic operator on a bounded domain $\Omega$ by the largest mean first ... -
Accelerated sampling by infinite swapping of path integral molecular dynamics with surface hopping
(2017-11-30)To accelerate the thermal equilibrium sampling of multi-level quantum systems, the infinite swapping limit of a recently proposed multi-level ring polymer representation is investigated. In the infinite swapping limiting, ... -
An isoperimetric problem with Coulomb repulsion and attraction to a background nucleus
(2017-04-23)We study an isoperimetric problem the energy of which contains the perimeter of a set, Coulomb repulsion of the set with itself, and attraction of the set to a background nucleus as a point charge with charge $Z$. For the ... -
Bloch dynamics with second order Berry phase correction
(2017-04-23)We derive the semiclassical Bloch dynamics with the second order Berry phase correction, based on a two-scale WKB asymptotic analysis. For uniform external electric field, the bi-characteristics system after a positional ... -
Bold Diagrammatic Monte Carlo in the Lens of Stochastic Iterative Methods
(2017-11-30)This work aims at understanding of bold diagrammatic Monte Carlo (BDMC) methods for stochastic summation of Feynman diagrams from the angle of stochastic iterative methods. The convergence enhancement trick of the BDMC is ... -
Complexity of zigzag sampling algorithm for strongly log-concave distributions
We study the computational complexity of zigzag sampling algorithm for strongly log-concave distributions. The zigzag process has the advantage of not requiring time discretization for implementation, and that each ... -
Defect resonances of truncated crystal structures
Defects in the atomic structure of crystalline materials may spawn electronic bound states, known as \emph{defect states}, which decay rapidly away from the defect. Simplified models of defect states typically assume the ... -
Emergence of step flow from an atomistic scheme of epitaxial growth in 1+1 dimensions.
(Phys Rev E Stat Nonlin Soft Matter Phys, 2015-03)The Burton-Cabrera-Frank (BCF) model for the flow of line defects (steps) on crystal surfaces has offered useful insights into nanostructure evolution. This model has rested on phenomenological grounds. Our goal is to show ... -
Existence and computation of generalized Wannier functions for non-periodic systems in two dimensions and higher
Exponentially-localized Wannier functions (ELWFs) are a basis of the Fermi projection of a material consisting of functions which decay exponentially fast away from their maxima. When the material is insulating ... -
Fast algorithm for periodic density fitting for Bloch waves
(2017-04-23)We propose an efficient algorithm for density fitting of Bloch waves for Hamiltonian operators with periodic potential. The algorithm is based on column selection and random Fourier projection of the orbital functions. The ... -
Fractional stochastic differential equations satisfying fluctuation-dissipation theorem
(2017-04-23)We consider in this work stochastic differential equation (SDE) model for particles in contact with a heat bath when the memory effects are non-negligible. As a result of the fluctuation-dissipation theorem, the differential ... -
Global optimality of softmax policy gradient with single hidden layer neural networks in the mean-field regime
We study the problem of policy optimization for infinite-horizon discounted Markov Decision Processes with softmax policy and nonlinear function approximation trained with policy gradient algorithms. We concentrate ... -
Improved sampling and validation of frozen Gaussian approximation with surface hopping algorithm for nonadiabatic dynamics.
(J Chem Phys, 2016-09-28)In the spirit of the fewest switches surface hopping, the frozen Gaussian approximation with surface hopping (FGA-SH) method samples a path integral representation of the non-adiabatic dynamics in the semiclassical regime. ... -
Infinite swapping replica exchange molecular dynamics leads to a simple simulation patch using mixture potentials.
(J Chem Phys, 2013-02-28)Replica exchange molecular dynamics (REMD) becomes more efficient as the frequency of swap between the temperatures is increased. Recently Plattner et al. [J. Chem. Phys. 135, 134111 (2011)] proposed a method to implement ... -
Non-Convex Planar Harmonic Maps
We formulate a novel characterization of a family of invertible maps between two-dimensional domains. Our work follows two classic results: The Rad\'o-Kneser-Choquet (RKC) theorem, which establishes the invertibility of harmonic ... -
On discrete Wigner transforms
In this work, we derive a discrete analog of the Wigner transform over the space $(\mathbb{C}^p)^{\otimes N}$ for any prime $p$ and any positive integer $N$. We show that the Wigner transform over this space can be constructed ... -
On explicit $L^2$-convergence rate estimate for piecewise deterministic Markov processes
We establish $L^2$-exponential convergence rate for three popular piecewise deterministic Markov processes for sampling: the randomized Hamiltonian Monte Carlo method, the zigzag process, and the bouncy particle sampler. ... -
On explicit $L^2$-convergence rate estimate for underdamped Langevin dynamics
We provide a new explicit estimate of exponential decay rate of underdamped Langevin dynamics in $L^2$ distance. To achieve this, we first prove a Poincar\'{e}-type inequality with Gibbs measure in space and Gaussian measure in ...
