18 citations · 55 across the 16 of their papers we have counts for
18 papers
Strong Duality Thresholds and Minimum Curvature for the Nearest Rectangular Symplectic Matrix Problem
Yulin Xie, Aiqing Zhu, Yifa Tang
We study the nearest rectangular symplectic matrix problem in the squared Frobenius norm for arbitrary targets , with . We prove that its semide…
Learning Operators of Geometry with an Interface Autoencoder
Aiqing Zhu, Pengzhan Jin
Geometry-dependent PDEs define operators whose inputs and outputs may each consist of an oriented interface and a function on that interface, whereas most existing neural operators…
Learning symplectic model reduction based on an approximation theorem of symplectic embeddings
Liyi Feng, Yifa Tang, Yulin Xie +2
High-dimensional Hamiltonian systems play a central role in many scientific and engineering disciplines, with dynamics that evolve on symplectic manifolds. Although deep learning p…
Calculating Domain of Attraction Boundary of Power Systems Based on the Gentlest Ascent Dynamics
Sixu Wu, Chenmin Zhang, Aiqing Zhu +3
The power system, a fundamental public utility, is increasingly important due to growing global electricity demand. Recent large-scale blackouts (e.g., Iberian Peninsula, UK) have…
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…
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…
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…