Zobrazeno 1 - 10
of 83
pro vyhledávání: '"Zhu, Aiqing"'
Autor:
Zhu, Aiqing, Li, Qianxiao
Learning unknown stochastic differential equations (SDEs) from observed data is a significant and challenging task with applications in various fields. Current approaches often use neural networks to represent drift and diffusion functions, and const
Externí odkaz:
http://arxiv.org/abs/2402.14475
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 propose an interfaced operator network (IONet) to solve parametric elliptic
Externí odkaz:
http://arxiv.org/abs/2308.14537
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 some predictor-corrector methods and structure-preserving methods for a
Externí odkaz:
http://arxiv.org/abs/2304.10882
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 the ODE-nets using unrolled implicit schemes for ease of interpretation
Externí odkaz:
http://arxiv.org/abs/2303.17824
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 established the grid error estimation with auxiliary conditions for the
Externí odkaz:
http://arxiv.org/abs/2209.12123
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 conservation properties. They are based on extending the original phase space
Externí odkaz:
http://arxiv.org/abs/2208.03875
The combination of ordinary differential equations and neural networks, i.e., neural ordinary differential equations (Neural ODE), has been widely studied from various angles. However, deciphering the numerical integration in Neural ODE is still an o
Externí odkaz:
http://arxiv.org/abs/2206.07335
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 the Poisson integrators can be constructed by using the splitting meth
Externí odkaz:
http://arxiv.org/abs/2205.05281
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 network architectures, coined R-VPNet and LA-VPNet. The distinct feature
Externí odkaz:
http://arxiv.org/abs/2204.13843
Publikováno v:
In Journal of Computational Physics 1 October 2024 514
