The method of fundamental solutions(MFS)and the Collocation Trefftz method have been known as two highly effective boundary-type methods for solving homogeneous equations.Despite many attractive features of these two ...The method of fundamental solutions(MFS)and the Collocation Trefftz method have been known as two highly effective boundary-type methods for solving homogeneous equations.Despite many attractive features of these two methods,they also experience different aspects of difficulty.Recent advances in the selection of source location of theMFS and the techniques in reducing the condition number of the Trefftz method have made significant improvement in the performance of these two methods which have been proven to be theoretically equivalent.In this paper we will compare the numerical performance of these two methods under various smoothness of the boundary and boundary conditions.展开更多
Multifdelity surrogates(MFSs)replace computationally intensive models by synergistically combining information from diferent fdelity data with a signifcant improvement in modeling efciency.In this paper,a modifed MFS(...Multifdelity surrogates(MFSs)replace computationally intensive models by synergistically combining information from diferent fdelity data with a signifcant improvement in modeling efciency.In this paper,a modifed MFS(MMFS)model based on a radial basis function(RBF)is proposed,in which two fdelities of information can be analyzed by adaptively obtaining the scale factor.In the MMFS,an RBF was employed to establish the low-fdelity model.The correlation matrix of the high-fdelity samples and corresponding low-fdelity responses were integrated into an expansion matrix to determine the scaling function parameters.The shape parameters of the basis function were optimized by minimizing the leave-one-out cross-validation error of the high-fdelity sample points.The performance of the MMFS was compared with those of other MFS models(MFS-RBF and cooperative RBF)and single-fdelity RBF using four benchmark test functions,by which the impacts of diferent high-fdelity sample sizes on the prediction accuracy were also analyzed.The sensitivity of the MMFS model to the randomness of the design of experiments(DoE)was investigated by repeating sampling plans with 20 diferent DoEs.Stress analysis of the steel plate is presented to highlight the prediction ability of the proposed MMFS model.This research proposes a new multifdelity modeling method that can fully use two fdelity sample sets,rapidly calculate model parameters,and exhibit good prediction accuracy and robustness.展开更多
The support vector classification （SVC） was employed to make a model for classification of antifungal activities of 1-（1H-1,2,4-triazole-l-yl）-2-（2,4-difluorophenyl）-3-substituted-2-propanols triazole derivative...The support vector classification （SVC） was employed to make a model for classification of antifungal activities of 1-（1H-1,2,4-triazole-l-yl）-2-（2,4-difluorophenyl）-3-substituted-2-propanols triazole derivatives. The compounds with high antifungal activities and those with low antifungal activities were compared on the basis of the following molecular descriptors： net atomic charge on the atom N connecting with R, dipole moment and heat of formation, By using the SVC, a mathematical model was constructed, which can predict the antifungal activities of the triazole derivatives, with an accuracy of 91% on the basis of the leave-one-out cross-validation （LOOCV） test, The results indicate that the performance of the SVC model can exceed that of the principal component analysis （PCA） and K-Nearest Neighbor （KNN） models for this real world data set.展开更多
基金Authors acknowledge the support of the Soft Science Project of Shanxi Province of China(Project No.2016041029-5)the National Natural Science Foundation of China(Grant No.11472184)the National Youth Science Foundation of China(Grant No.11401423).
文摘The method of fundamental solutions(MFS)and the Collocation Trefftz method have been known as two highly effective boundary-type methods for solving homogeneous equations.Despite many attractive features of these two methods,they also experience different aspects of difficulty.Recent advances in the selection of source location of theMFS and the techniques in reducing the condition number of the Trefftz method have made significant improvement in the performance of these two methods which have been proven to be theoretically equivalent.In this paper we will compare the numerical performance of these two methods under various smoothness of the boundary and boundary conditions.
基金Supported by National Key R&D Program of China(Grant No.2018YFB1700704).
文摘Multifdelity surrogates(MFSs)replace computationally intensive models by synergistically combining information from diferent fdelity data with a signifcant improvement in modeling efciency.In this paper,a modifed MFS(MMFS)model based on a radial basis function(RBF)is proposed,in which two fdelities of information can be analyzed by adaptively obtaining the scale factor.In the MMFS,an RBF was employed to establish the low-fdelity model.The correlation matrix of the high-fdelity samples and corresponding low-fdelity responses were integrated into an expansion matrix to determine the scaling function parameters.The shape parameters of the basis function were optimized by minimizing the leave-one-out cross-validation error of the high-fdelity sample points.The performance of the MMFS was compared with those of other MFS models(MFS-RBF and cooperative RBF)and single-fdelity RBF using four benchmark test functions,by which the impacts of diferent high-fdelity sample sizes on the prediction accuracy were also analyzed.The sensitivity of the MMFS model to the randomness of the design of experiments(DoE)was investigated by repeating sampling plans with 20 diferent DoEs.Stress analysis of the steel plate is presented to highlight the prediction ability of the proposed MMFS model.This research proposes a new multifdelity modeling method that can fully use two fdelity sample sets,rapidly calculate model parameters,and exhibit good prediction accuracy and robustness.
基金Project supported by the National Natural Science Foundation of China （Grant Nos.20373040, 20503015）
文摘The support vector classification （SVC） was employed to make a model for classification of antifungal activities of 1-（1H-1,2,4-triazole-l-yl）-2-（2,4-difluorophenyl）-3-substituted-2-propanols triazole derivatives. The compounds with high antifungal activities and those with low antifungal activities were compared on the basis of the following molecular descriptors： net atomic charge on the atom N connecting with R, dipole moment and heat of formation, By using the SVC, a mathematical model was constructed, which can predict the antifungal activities of the triazole derivatives, with an accuracy of 91% on the basis of the leave-one-out cross-validation （LOOCV） test, The results indicate that the performance of the SVC model can exceed that of the principal component analysis （PCA） and K-Nearest Neighbor （KNN） models for this real world data set.
