4 papers
Physics-informed neural networks for solving two-phase flow problems with moving interfaces
Qijia Zhai, Pengtao Sun, Xiaoping Xie +2
In this paper, a meshfree method using physics-informed neural networks (PINNs) is developed for solving two-phase flow problems with moving interfaces, where two immiscible fluids…
A Domain Decomposition Deep Neural Network Method with Multi-Activation Functions for Solving Elliptic and Parabolic Interface Problems
Qijia Zhai
We present a domain decomposition-based deep learning method for solving elliptic and parabolic interface problems with discontinuous coefficients in two to ten dimensions. Our Mul…
Is the Frequency Principle always valid?
Qijia Zhai
We investigate the learning dynamics of shallow ReLU neural networks on the unit sphere \(S^2\subset\mathbb{R}^3\) in polar coordinates \((τ,ϕ)\), considering both fixed and traina…
Robust globally divergence-free HDG finite element method for steady thermally coupled incompressible MHD flow
Min Zhang, Zimo Zhu, Qijia Zhai +1
This paper develops an hybridizable discontinuous Galerkin (HDG) finite element method of arbitrary order for the steady thermally coupled incompressible Magnetohydrodynamics (MHD)…