9 papers
A transition-density-based operator learning method for Fokker-Planck equations with various initial conditions
Li Zeng, Xiaoliang Wan, Yaobin Wang +2
Solving Fokker-Planck equations (FPEs) for multiple initial conditions typically requires repeated computations, leading to substantial computational costs. In this work, we propos…
A modified projected walk on spheres method for elliptic equations on high-dimensional embedded manifolds: algorithm and error estimates
Zhiyuan Hui, Changtao Sheng, Bihao Su +1
In this paper, we propose a modified projected Walk on Spheres method (MPWoS) for screened Poisson equations on embedded manifolds. The method employs local extensions together wit…
Towards Robust EEG Decoding Based on Riemannian Self-Attention
Shaocheng Jin, Tao Zhou, Rui Wang +4
Brain-Computer Interface (BCI) based on electroencephalography (EEG) enables direct interaction between the brain and external environments and has significant applications in assi…
PI-DOSnet: A Physics-Informed Deep Operator-Splitting Network for Evolution Partial Differential Equations
Jizu Huang, Yue Qian, Tao Zhou
Evolution partial differential equations (PDEs) describe time-dependent physical systems governed by differential laws and arise widely across science and engineering. In recent ye…
On the stability of Lamb-Chaplygin dipole for the 2D Euler equation
Zexing Li, Peicong Song, Tao Zhou
The Lamb-Chaplygin dipole is a traveling wave solution to the 2D incompressible Euler equation, whose orbital stability was established in [Abe-Choi, 2022] and [Abe-Choi-Jeong, 202…
Decoupled Divergence-Free Neural Networks Basis Method for Incompressible Fluid Problems
Jinbao Cheng, Jianguo Huang, Haoqin Wang +1
We propose a decoupled divergence-free neural networks basis (Decoupled-DFNN) method for solving incompressible flow problems, including the Stokes and Navier-Stokes equations. To…
Deep learning for the semi-classical limit of the Schrödinger equation
Jizu Huang, Rukang You, Tao Zhou
In this paper, we integrate neural networks and Gaussian wave packets to numerically solve the Schrödinger equation with a smooth potential near the semi-classical limit. Our focus…
Frequency-adaptive tensor neural networks for high-dimensional multi-scale problems
Jizu Huang, Yue Qiu, Rukang You
Tensor neural networks (TNNs) have demonstrated their superiority in solving high-dimensional problems. However, similar to conventional neural networks, TNNs are also influenced b…
Frequency-adaptive Multi-scale Deep Neural Networks
Jizu Huang, Rukang You, Tao Zhou
Multi-scale deep neural networks (MscaleDNNs) with downing-scaling mapping have demonstrated superiority over traditional DNNs in approximating target functions characterized by hi…