7 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)…
A Projection-Based Time-Segmented Reduced Order Model for Fluid-Structure Interactions
Qijia Zhai, Shiquan Zhang, Pengtao Sun +1
In this paper, a type of novel projection-based, time-segmented reduced order model (ROM) is proposed for dynamic fluid-structure interaction (FSI) problems based upon the arbitrar…
A Priori Error Estimation of Physics-Informed Neural Networks Solving Allen--Cahn and Cahn--Hilliard Equations
Guangtao Zhang, Jiani Lin, Qijia Zhai +4
Physics-Informed Neural Networks (PINNs) encounter accuracy limitations when solving the Allen--Cahn (AC) and Cahn--Hilliard (CH) partial differential equations (PDEs). To overcome…
A New Reduced Basis Method for Parabolic Equations Based on Single-Eigenvalue Acceleration
Qijia Zhai, Qingguo Hong, Xiaoping Xie
In this paper, we develop a new reduced basis (RB) method, named as Single Eigenvalue Acceleration Method (SEAM), for second-order parabolic equations with homogeneous Dirichlet bo…