71 citations · 207 across the 22 of their papers we have counts for
8 papers · 1 filter
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…