4 papers
Dynamical low-rank approximation for the semiclassical Schrodinger equation with uncertainties
Liu Liu, Limin Xu, Zhenyi Zhu
In this paper, we propose a dynamical low-rank (DLR) approximation framework for solving the semiclassical Schrodinger equation with uncertainties. The primary numerical challenges…
A Bi-fidelity based asymptotic-preserving neural network for the semiconductor Boltzmann equation and its inverse problem
Liu Liu, Xueyu Zhu, Zhenyi Zhu
This paper introduces a Bi-fidelity Asymptotic-Preserving Neural Network (BI-APNNs) framework, designed to efficiently solve forward and inverse problems for the semiconductor Bolt…
Deep learning-based moment closure for multi-phase computation of semiclassical limit of the Schrödinger equation
Jin Woo Jang, Jae Yong Lee, Liu Liu +1
We present a deep learning approach for computing multi-phase solutions to the semiclassical limit of the Schrödinger equation. Traditional methods require deriving a multi-phase a…
PhysicsSolver: Transformer-Enhanced Physics-Informed Neural Networks for Forward and Forecasting Problems in Partial Differential Equations
Zhenyi Zhu, Yuchen Huang, Liu Liu
Time-dependent partial differential equations are a significant class of equations that describe the evolution of various physical phenomena over time. One of the open problems in…