71 citations · 207 across the 22 of their papers we have counts for
22 papers
Modified-gradient methods for exact divergence-free in meshless magnetohydrodynamics
Xiongbiao Tu, Qiao Wang, Liang Gao +1
We present a novel gradient regularization to completely eliminate the magnetic divergence error in meshless magnetohydrodynamics (MHD), which offers a high spatial resolution and…
Solving parametric elliptic interface problems via interfaced operator network
Sidi Wu, Aiqing Zhu, Yifa Tang +1
Learning operators mapping between infinite-dimensional Banach spaces via neural networks has attracted a considerable amount of attention in recent years. In this paper, we propos…
Effective Numerical Simulations of Synchronous Generator System
Jiawei Zhang, Aiqing Zhu, Feng Ji +2
Synchronous generator system is a complicated dynamical system for energy transmission, which plays an important role in modern industrial production. In this article, we propose s…
Implementation and (Inverse Modified) Error Analysis for implicitly-templated ODE-nets
Aiqing Zhu, Tom Bertalan, Beibei Zhu +2
We focus on learning unknown dynamics from data using ODE-nets templated on implicit numerical initial value problem solvers. First, we perform Inverse Modified error analysis of t…
Error analysis based on inverse modified differential equations for discovery of dynamics using linear multistep methods and deep learning
Aiqing Zhu, Sidi Wu, Yifa Tang
Along with the practical success of the discovery of dynamics using deep learning, the theoretical analysis of this approach has attracted increasing attention. Prior works have es…
Explicit K-symplectic methods for nonseparable non-canonical Hamiltonian systems
Beibei Zhu, Lun Ji, Aiqing Zhu +1
We propose efficient numerical methods for nonseparable non-canonical Hamiltonian systems which are explicit, K-symplectic in the extended phase space with long time energy conserv…
On Numerical Integration in Neural Ordinary Differential Equations
Aiqing Zhu, Pengzhan Jin, Beibei Zhu +1
The combination of ordinary differential equations and neural networks, i.e., neural ordinary differential equations (Neural ODE), has been widely studied from various angles. Howe…
Poisson Integrators based on splitting method for Poisson systems
Beibei Zhu, Lun Ji, Aiqing Zhu +1
We propose Poisson integrators for the numerical integration of separable Poisson systems. We analyze three situations in which the Poisson systems are separated in three ways and…
A modified EM method and its fast implementation for multi-term Riemann-Liouville stochastic fractional differential equations
Jingna Zhang, Jianfei Huang, Yifa Tang +1
In this paper, a modified Euler-Maruyama (EM) method is constructed for a kind of multi-term Riemann-Liouville stochastic fractional differential equations and the strong convergen…
VPNets: Volume-preserving neural networks for learning source-free dynamics
Aiqing Zhu, Beibei Zhu, Jiawei Zhang +2
We propose volume-preserving networks (VPNets) for learning unknown source-free dynamical systems using trajectory data. We propose three modules and combine them to obtain two net…
Convergence of physics-informed neural networks applied to linear second-order elliptic interface problems
Sidi Wu, Aiqing Zhu, Yifa Tang +1
With the remarkable empirical success of neural networks across diverse scientific disciplines, rigorous error and convergence analysis are also being developed and enriched. Howev…
Symplectic Integrators in Corotating Coordinates
Xiongbiao Tu, Qiao Wang, Yifa Tang
The dynamic equation of mass point in rotating coordinates is governed by Coriolis and centrifugal force, besides a corotating potential relative to frame. Such a system is no long…
Approximation capabilities of measure-preserving neural networks
Aiqing Zhu, Pengzhan Jin, Yifa Tang
Measure-preserving neural networks are well-developed invertible models, however, their approximation capabilities remain unexplored. This paper rigorously analyses the approximati…
Inverse modified differential equations for discovery of dynamics
Aiqing Zhu, Pengzhan Jin, Beibei Zhu +1
The combination of numerical integration and deep learning, i.e., ODE-net, has been successfully employed in a variety of applications. In this work, we introduce inverse modified…
Deep Hamiltonian networks based on symplectic integrators
Aiqing Zhu, Pengzhan Jin, Yifa Tang
HNets is a class of neural networks on grounds of physical prior for learning Hamiltonian systems. This paper explains the influences of different integrators as hyper-parameters o…
SympNets: Intrinsic structure-preserving symplectic networks for identifying Hamiltonian systems
Pengzhan Jin, Zhen Zhang, Aiqing Zhu +2
We propose new symplectic networks (SympNets) for identifying Hamiltonian systems from data based on a composition of linear, activation and gradient modules. In particular, we def…
Unit triangular factorization of the matrix symplectic group
Pengzhan Jin, Yifa Tang, Aiqing Zhu
In this work, we prove that any symplectic matrix can be factored into no more than 9 unit triangular symplectic matrices. This structure-preserving factorization of the symplectic…
Spectrally accurate space-time solution of Manakov systems
Luigi Barletti, Luigi Brugnano, Yifa Tang +1
In this paper, we study the numerical solution of Manakov systems by using a spectrally accurate Fourier decomposition in space, coupled with a spectrally accurate time integration…
Explicit symplectic algorithms based on generating functions for relativistic charged particle dynamics in time-dependent electromagnetic field
Ruili Zhang, Yulei Wang, Yang He +4
Relativistic dynamics of a charged particle in time-dependent electromagnetic fields has theoretical significance and a wide range of applications. It is often multi-scale and requ…
Explicit symplectic algorithms based on generating functions for charged particle dynamics
Ruili Zhang, Hong Qin, Yifa Tang +3
Dynamics of a charged particle in the canonical coordinates is a Hamiltonian system, and the well-known symplectic algorithm has been regarded as the de facto method for numerical…
Symplectic methods for non-canonical Hamiltonian systems
Beibei Zhu, Ruili Zhang, Yifa Tang +1
We show that, when applied to any non-canonical Hamiltonian system, any integrator that is symplectic for canonical Hamiltonian problems is actually conjugate symplectic for the no…
The spread of disease with birth and death on networks
Jingzhou Liu
In this paper, we introduce a modified epidemic model on regular and scale-free networks respectively. We consider the birth rate , cure rate , infection rate , from t…