Neural networks based on power method and inverse power method for solving linear eigenvalue problems
Q Yang, Y Deng, Y Yang, Q He, S Zhang - Computers & Mathematics with …, 2023 - Elsevier
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 …
inverse power method to solve linear eigenvalue problems. These neural networks share …
Discovery of Quasi-Integrable Equations from traveling-wave data using the Physics-Informed Neural Networks
A Nakamula, N Sawado, K Shimasaki… - arXiv preprint arXiv …, 2024 - arxiv.org
Physics-Informed Neural Networks (PINNs) are used to study vortex solutions in the 2+ 1
dimensional nonlinear partial differential equations. These solutions include the regularized …
dimensional nonlinear partial differential equations. These solutions include the regularized …
On the uncertainty analysis of the data-enabled physics-informed neural network for solving neutron diffusion eigenvalue problem
We performed uncertainty analysis and further numerical studies on the data-enabled
physics-informed neural network (DEPINN). The purpose of DEPINN is to accurately and …
physics-informed neural network (DEPINN). The purpose of DEPINN is to accurately and …
Physics-constrained neural network for solving discontinuous interface K-eigenvalue problem with application to reactor physics
Abstract Machine learning-based modeling of reactor physics problems has attracted
increasing interest in recent years. Despite some progress in one-dimensional problems …
increasing interest in recent years. Despite some progress in one-dimensional problems …
Residual resampling-based physics-informed neural network for neutron diffusion equations
H Zhang, YL He, D Liu, Q Hang, HM Yao… - arXiv preprint arXiv …, 2024 - arxiv.org
The neutron diffusion equation plays a pivotal role in the analysis of nuclear reactors.
Nevertheless, employing the Physics-Informed Neural Network (PINN) method for its …
Nevertheless, employing the Physics-Informed Neural Network (PINN) method for its …
[HTML][HTML] A Data Assimilation Methodology to Analyze the Unsaturated Seepage of an Earth–Rockfill Dam Using Physics-Informed Neural Networks Based on Hybrid …
Q Dai, W Zhou, R He, J Yang, B Zhang, Y Lei - Water, 2024 - mdpi.com
Data assimilation for unconfined seepage analysis has faced significant challenges due to
hybrid causes, such as sparse measurements, heterogeneity of porous media, and …
hybrid causes, such as sparse measurements, heterogeneity of porous media, and …
[HTML][HTML] A multi-scale finite element method for neutron diffusion eigenvalue problem
In this paper, we propose a multi-scale finite element method for solving the two-group
neutron diffusion equation, which represents the distribution of neutrons in thermal reactors …
neutron diffusion equation, which represents the distribution of neutrons in thermal reactors …
Research on least-square solver for physics-informed neural network in thermal-hydraulic analysis of nuclear reactors
W Bo, X Li, X Zhou, Z Dalin, T Wenxi, Q Suizheng… - Annals of Nuclear …, 2025 - Elsevier
Abstract Physics-Informed Neural Network (PINN) integrates Deep Neural Networks (DNN)
with physical principles to solve complex physical systems. While its computational accuracy …
with physical principles to solve complex physical systems. While its computational accuracy …
Optimizing near-carbon-free nuclear energy systems: advances in reactor operation digital twin through hybrid machine learning algorithms for parameter …
Accurate and efficient online parameter identification and state estimation are crucial for
leveraging digital twin simulations to optimize the operation of near-carbon-free nuclear …
leveraging digital twin simulations to optimize the operation of near-carbon-free nuclear …
[HTML][HTML] 深度学习在边界层流动稳定性分析中的应用
樊佳坤， 姚方舟， 黄江涛， 徐家宽， 乔磊… - 空气动力学学报, 2023 - pubs.cstam.org.cn
基于线性稳定性理论(linear stability theory, LST) 的e N 方法是边界层转捩预测中比较可靠的
方法之一. 为了将传统LST 特征值问题的求解过程大幅度简化和自动化, 使用卷积神经网络 …
方法之一. 为了将传统LST 特征值问题的求解过程大幅度简化和自动化, 使用卷积神经网络 …