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math.NA2023
A synchronization-capturing multi-scale solver to the noisy integrate-and-fire neuron networks
Ziyu Du, Yantong Xie, Zhennan Zhou
The noisy leaky integrate-and-fire (NLIF) model describes the voltage configurations of neuron networks with an interacting many-particles system at a microscopic level. When simul…
math.NA2021
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…
math.NA2019
A structure preserving numerical scheme for Fokker-Planck equations of neuron networks: numerical analysis and exploration
Jingwei Hu, Jian-Guo Liu, Yantong Xie +1
In this work, we are concerned with the Fokker-Planck equations associated with the Nonlinear Noisy Leaky Integrate-and-Fire model for neuron networks. Due to the jump mechanism at…