33 citations · 179 across the 44 of their papers we have counts for
7 papers · 1 filter
Frozen Gaussian Sampling: A Mesh-free Monte Carlo Method For Approximating Semiclassical Schrödinger Equations
Yantong Xie, Zhennan Zhou
In this paper, we develop a Monte Carlo algorithm named the Frozen Gaussian Sampling (FGS) to solve the semiclassical Schrödinger equation based on the frozen Gaussian approximatio…
A structure preserving numerical scheme for Fokker-Planck equations of structured neural networks with learning rules
Qing He, Jingwei Hu, Zhennan Zhou
In this work, we are concerned with a Fokker-Planck equation related to the nonlinear noisy leaky integrate-and-fire model for biological neural networks which are structured by th…
A Mean Field Game Analysis of Consensus Protocol Design
Lucy Klinger, Lei Zhang, Zhennan Zhou
A decentralized blockchain is a distributed ledger that is often used as a platform for exchanging goods and services. This ledger is maintained by a network of nodes that obeys a…
Fast Algorithms and Error Analysis of Caputo Derivatives with Small Factional Orders
Zihang Zhang, Qiwei Zhan, Zhennan Zhou
In this paper, we investigate fast algorithms in the small fraction order regime to approximate the Caputo derivative when is small. We focus on two fast algori…
Efficient Sampling of Thermal Averages of Interacting Quantum Particle Systems with Random Batches
Xuda Ye, Zhennan Zhou
An efficient sampling method, the pmmLang+RBM, is proposed to compute the quantum thermal average in the interacting quantum particle system. Benefiting from the random batch metho…
Investigating the integrate and fire model as the limit of a random discharge model: a stochastic analysis perspective
Jian-Guo Liu, Ziheng Wang, Yantong Xie +2
In the mean field integrate-and-fire model, the dynamics of a typical neuron within a large network is modeled as a diffusion-jump stochastic process whose jump takes place once th…
A novel spectral method for the semi-classical Schrödinger equation based on the Gaussian wave-packet transform
Borui Miao, Giovanni Russo, Zhennan Zhou
In this article, we develop and analyse a new spectral method to solve the semi-classical Schrödinger equation based on the Gaussian wave-packet transform (GWPT) and Hagedorn's sem…