18 citations · 55 across the 16 of their papers we have counts for
10 papers · 1 filter
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…
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…
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…
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…
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…