为准确求解双曲守恒律,得到高分辨率数值结果,将数据驱动与三阶CCWENO(Compact Central Weighted Essentially Non-Oscillatory)格式相结合,提出了一种基于数据驱动的CCWENO-ANN高分辨率格式求解双曲守恒律。通过构建人工神经网络的归...为准确求解双曲守恒律,得到高分辨率数值结果,将数据驱动与三阶CCWENO(Compact Central Weighted Essentially Non-Oscillatory)格式相结合,提出了一种基于数据驱动的CCWENO-ANN高分辨率格式求解双曲守恒律。通过构建人工神经网络的归一化校准层和稀疏化层,引入适当的先验知识,加快收敛速度;同时,损失函数动态地调整神经网络输出与理想权重之间的偏差,并在合适的数据集上采用监督学习策略进行离线训练,以提高神经网络性能。通过一维无粘Burgers方程、一维Euler方程、二维无粘Burgers方程以及二维Euler方程验证算法性能,结果表明本文提出的CCWENO-ANN继承了传统CCWENO格式的收敛性,能够准确捕捉激波和接触间断,具有鲁棒性强、低耗散和高分辨率的优点。展开更多
Gauss radial basis functions(GRBF)are frequently employed in data fitting and machine learning.Their linear independence property can theoretically guarantee the avoidance of data redundancy.In this paper,one of the m...Gauss radial basis functions(GRBF)are frequently employed in data fitting and machine learning.Their linear independence property can theoretically guarantee the avoidance of data redundancy.In this paper,one of the main contributions is proving this property using linear algebra instead of profound knowledge.This makes it easy to read and understand this fundamental fact.The proof of linear independence of a set of Gauss functions relies on the constructing method for one-dimensional space and on the deducing method for higher dimensions.Additionally,under the condition of preserving the same moments between the original function and interpolating function,both the interpolating existence and uniqueness are proven for GRBF in one-dimensional space.The final work demonstrates the application of the GRBF method to locate lunar olivine.By combining preprocessed data using GRBF with the removing envelope curve method,a program is created to find the position of lunar olivine based on spectrum data,and the numerical experiment shows that it is an effective scheme.展开更多
In this paper,we consider the maximal positive definite solution of the nonlinear matrix equation.By using the idea of Algorithm 2.1 in ZHANG(2013),a new inversion-free method with a stepsize parameter is proposed to ...In this paper,we consider the maximal positive definite solution of the nonlinear matrix equation.By using the idea of Algorithm 2.1 in ZHANG(2013),a new inversion-free method with a stepsize parameter is proposed to obtain the maximal positive definite solution of nonlinear matrix equation X+A^(*)X|^(-α)A=Q with the case 0<α≤1.Based on this method,a new iterative algorithm is developed,and its convergence proof is given.Finally,two numerical examples are provided to show the effectiveness of the proposed method.展开更多
文摘为准确求解双曲守恒律,得到高分辨率数值结果,将数据驱动与三阶CCWENO(Compact Central Weighted Essentially Non-Oscillatory)格式相结合,提出了一种基于数据驱动的CCWENO-ANN高分辨率格式求解双曲守恒律。通过构建人工神经网络的归一化校准层和稀疏化层,引入适当的先验知识,加快收敛速度;同时,损失函数动态地调整神经网络输出与理想权重之间的偏差,并在合适的数据集上采用监督学习策略进行离线训练,以提高神经网络性能。通过一维无粘Burgers方程、一维Euler方程、二维无粘Burgers方程以及二维Euler方程验证算法性能,结果表明本文提出的CCWENO-ANN继承了传统CCWENO格式的收敛性,能够准确捕捉激波和接触间断,具有鲁棒性强、低耗散和高分辨率的优点。
基金Supported by the National Basic Research Program of China(2012CB025904)Zhengzhou Shengda University of Economics,Business and Management(SD-YB2025085)。
文摘Gauss radial basis functions(GRBF)are frequently employed in data fitting and machine learning.Their linear independence property can theoretically guarantee the avoidance of data redundancy.In this paper,one of the main contributions is proving this property using linear algebra instead of profound knowledge.This makes it easy to read and understand this fundamental fact.The proof of linear independence of a set of Gauss functions relies on the constructing method for one-dimensional space and on the deducing method for higher dimensions.Additionally,under the condition of preserving the same moments between the original function and interpolating function,both the interpolating existence and uniqueness are proven for GRBF in one-dimensional space.The final work demonstrates the application of the GRBF method to locate lunar olivine.By combining preprocessed data using GRBF with the removing envelope curve method,a program is created to find the position of lunar olivine based on spectrum data,and the numerical experiment shows that it is an effective scheme.
基金Supported in part by Natural Science Foundation of Guangxi(2023GXNSFAA026246)in part by the Central Government's Guide to Local Science and Technology Development Fund(GuikeZY23055044)in part by the National Natural Science Foundation of China(62363003)。
文摘In this paper,we consider the maximal positive definite solution of the nonlinear matrix equation.By using the idea of Algorithm 2.1 in ZHANG(2013),a new inversion-free method with a stepsize parameter is proposed to obtain the maximal positive definite solution of nonlinear matrix equation X+A^(*)X|^(-α)A=Q with the case 0<α≤1.Based on this method,a new iterative algorithm is developed,and its convergence proof is given.Finally,two numerical examples are provided to show the effectiveness of the proposed method.
