7 citations · 18 across the 8 of their papers we have counts for
8 papers
On the uncertainty analysis of the data-enabled physics-informed neural network for solving neutron diffusion eigenvalue problem
Yu Yang, Helin Gong, Qihong Yang +3
In practical engineering experiments, the data obtained through detectors are inevitably noisy. For the already proposed data-enabled physics-informed neural network (DEPINN) \cite…
Neural Networks Based on Power Method and Inverse Power Method for Solving Linear Eigenvalue Problems
Qihong Yang, Yangtao Deng, Yu Yang +2
In this article, we propose two kinds of neural networks inspired by power method and inverse power method to solve linear eigenvalue problems. These neural networks share similar…
A data-enabled physics-informed neural network with comprehensive numerical study on solving neutron diffusion eigenvalue problems
Yu Yang, Helin Gong, Shiquan Zhang +4
We present a data-enabled physics-informed neural network (DEPINN) with comprehensive numerical study for solving industrial scale neutron diffusion eigenvalue problems (NDEPs). In…
An Optimal Embedded Discontinuous Galerkin Method for Second-Order Elliptic Problems
Xiao Zhang, Xiaoping Xie, Shiquan Zhang
The embedded discontinuous Galerkin (EDG) method by Cockburn et al. [SIAM J. Numer. Anal., 2009, 47(4), 2686-2707] is obtained from the hybridizable discontinuous Galerkin method b…
A new smoothness result for Caputo-type fractional ordinary differential equations
Binjie Li, Xiaoping Xie, Shiquan Zhang
We present a new smoothness result for Caputo-type fractional ordinary differential equations, which reveals that, subtracting a non-smooth function that can be obtained by the inf…
Analysis of a two-level algorithm for HDG methods for diffusion problems
Binjie Li, Xiaoping Xie, Shiquan Zhang
This paper analyzes an abstract two-level algorithm for hybridizable discontinuous Galerkin (HDG) methods in a unified fashion. We use an extended version of the Xu-Zikatanov (X-Z)…
A Model Reduction Framework for Efficient Simulation of Li-Ion Batteries
Mario Ohlberger, Stephan Rave, Sebastian Schmidt +1
In order to achieve a better understanding of degradation processes in lithium-ion batteries, the modelling of cell dynamics at the mircometer scale is an important focus of curren…
Combined Preconditioning with Applications in Reservoir Simulation
Xiaozhe Hu, Shuhong Wu, Xiao-Hui Wu +4
We develop a simple algorithmic framework to solve large-scale symmetric positive definite linear systems. At its core, the framework relies on two components: (1) a norm-convergen…