This paper applies a machine learning technique to find a general and efficient numerical integration scheme for boundary element methods.A model based on the neural network multi-classification algorithmis constructe...This paper applies a machine learning technique to find a general and efficient numerical integration scheme for boundary element methods.A model based on the neural network multi-classification algorithmis constructed to find the minimum number of Gaussian quadrature points satisfying the given accuracy.The constructed model is trained by using a large amount of data calculated in the traditional boundary element method and the optimal network architecture is selected.The two-dimensional potential problem of a circular structure is tested and analyzed based on the determined model,and the accuracy of the model is about 90%.Finally,by incorporating the predicted Gaussian quadrature points into the boundary element analysis,we find that the numerical solution and the analytical solution are in good agreement,which verifies the robustness of the proposed method.展开更多
In this paper,we introduce a type of tensor neural network.For the first time,we propose its numerical integration scheme and prove the computational complexity to be the polynomial scale of the dimension.Based on the...In this paper,we introduce a type of tensor neural network.For the first time,we propose its numerical integration scheme and prove the computational complexity to be the polynomial scale of the dimension.Based on the tensor product structure,we develop an efficient numerical integration method by using fixed quadrature points for the functions of the tensor neural network.The corresponding machine learning method is also introduced for solving high-dimensional problems.Some numerical examples are also provided to validate the theoretical results and the numerical algorithm.展开更多
基金The authors thank the financial support of National Natural Science Foundation of China(NSFC)under Grant(No.11702238).
文摘This paper applies a machine learning technique to find a general and efficient numerical integration scheme for boundary element methods.A model based on the neural network multi-classification algorithmis constructed to find the minimum number of Gaussian quadrature points satisfying the given accuracy.The constructed model is trained by using a large amount of data calculated in the traditional boundary element method and the optimal network architecture is selected.The two-dimensional potential problem of a circular structure is tested and analyzed based on the determined model,and the accuracy of the model is about 90%.Finally,by incorporating the predicted Gaussian quadrature points into the boundary element analysis,we find that the numerical solution and the analytical solution are in good agreement,which verifies the robustness of the proposed method.
基金supported in part by the National Key Research and Development Program of China(Grant No.2019YFA0709601)by the National Center for Mathematics and Interdisciplinary Science,CAS.
文摘In this paper,we introduce a type of tensor neural network.For the first time,we propose its numerical integration scheme and prove the computational complexity to be the polynomial scale of the dimension.Based on the tensor product structure,we develop an efficient numerical integration method by using fixed quadrature points for the functions of the tensor neural network.The corresponding machine learning method is also introduced for solving high-dimensional problems.Some numerical examples are also provided to validate the theoretical results and the numerical algorithm.
