In this paper, we develop an implicitly restarted block Arnoldi algorithm in a vector-wise fashion. The vector-wise construction greatly simplifies both the detection of necessary deflation and the actual deflation it...In this paper, we develop an implicitly restarted block Arnoldi algorithm in a vector-wise fashion. The vector-wise construction greatly simplifies both the detection of necessary deflation and the actual deflation itself, so it is preferable to the block-wise construction. The numerical experiment shows that our algorithm is effective.展开更多
神经隐式表征是一种新兴的形状表示范式,但多数传统隐式表示方法如DeepSDF等未考虑整体形状的局部特征信息,存在拓扑细节精度不足的问题。为解决上述问题,提出了一种由部件隐向量驱动的隐式三维重建方法,即构建部件的隐式场以最小化模...神经隐式表征是一种新兴的形状表示范式,但多数传统隐式表示方法如DeepSDF等未考虑整体形状的局部特征信息,存在拓扑细节精度不足的问题。为解决上述问题,提出了一种由部件隐向量驱动的隐式三维重建方法,即构建部件的隐式场以最小化模型预测的整体形状目标点有符号距离值LGI-RIF(Reconstruction of Implicit Fields with Local and Global Integration),能从观测数据中重建几何形状。该方法在一个低维的潜在编码空间中训练神经网络并在解码器框架中联合优化,设计EFP、EFCS和R3DS这3个模块,在EFP模块中由设计的变分自编码器学习部件的特征向量分布,在EFCS模块中构建自动解码器学习整体形状的SDF隐式表达,在R3DS模块中重建整体三维形状。实验结果表明:LGI-RIF在ShapeNet和ModelNet 10数据集上的重建精度得到了进一步提升,在可视化重构中具有良好的视觉效果。展开更多
In order to deal with the issue of huge computational cost very well in direct numerical simulation, the traditional response surface method (RSM) as a classical regression algorithm is used to approximate a functiona...In order to deal with the issue of huge computational cost very well in direct numerical simulation, the traditional response surface method (RSM) as a classical regression algorithm is used to approximate a functional relationship between the state variable and basic variables in reliability design. The algorithm has treated successfully some problems of implicit performance function in reliability analysis. However, its theoretical basis of empirical risk minimization narrows its range of applications for...展开更多
Support vector machine （SVM） was introduced to analyze the reliability of the implicit performance function, which is difficult to implement by the classical methods such as the first order reliability method （FORM...Support vector machine （SVM） was introduced to analyze the reliability of the implicit performance function, which is difficult to implement by the classical methods such as the first order reliability method （FORM） and the Monte Carlo simulation （MCS）. As a classification method where the underlying structural risk minimization inference rule is employed, SVM possesses excellent learning capacity with a small amount of information and good capability of generalization over the complete data. Hence, two approaches, i.e., SVM-based FORM and SVM-based MCS, were presented for the structural reliability analysis of the implicit limit state function. Compared to the conventional response surface method （RSM） and the artificial neural network （ANN）, which are widely used to replace the implicit state function for alleviating the computation cost, the more important advantages of SVM are that it can approximate the implicit function with higher precision and better generalization under the small amount of information and avoid the ＂curse of dimensionality＂. The SVM-based reliability approaches can approximate the actual performance function over the complete sampling data with the decreased number of the implicit performance function analysis （usually finite element analysis）, and the computational precision can satisfy the engineering requirement, which are demonstrated by illustrations.展开更多
The key problem in the computation of fluid dynamics using fine boundary-fitted grids is how to improve the numerical stability and decrease the calculating quantity. To solve this problem, implicit schemes should be ...The key problem in the computation of fluid dynamics using fine boundary-fitted grids is how to improve the numerical stability and decrease the calculating quantity. To solve this problem, implicit schemes should be adopted since explicit schemes may bring about a great increase in computation quantity according to the Courant-FrledrichsLewy condition. Whereas the adoption of implicit schemes is difficult to be realized because of the existence of two partial derivatives of surface elevations with respect to variables of alternative direction coordinates in each momentum equation in non-rectangular coordinates. With an aim to design an implicit scheme in non-reetangular ccordinates in the present paper, new momentum equations with the contravariant components of velocity vector are derived based on the shallow water dynamic equations in generalized curvilinear coordinates. In each equation, the coefficients before the two detivatives of surface elevations have different orders of magnitude, i. e., the derivative with the larger ceefficient rnay play a more important role than that with the smaller one. With this advantage, the ADI scheme can then be easily employed to improve the numerical stability and decrease the calculating quantity. The calculation in a harbour and a channel in Macau nearshore area shows that the implicit model is effective in calculating current fields in small size areas.展开更多
基金This work is supported by National Natural Science Foundation of China No. 10531080.
文摘In this paper, we develop an implicitly restarted block Arnoldi algorithm in a vector-wise fashion. The vector-wise construction greatly simplifies both the detection of necessary deflation and the actual deflation itself, so it is preferable to the block-wise construction. The numerical experiment shows that our algorithm is effective.
文摘神经隐式表征是一种新兴的形状表示范式,但多数传统隐式表示方法如DeepSDF等未考虑整体形状的局部特征信息,存在拓扑细节精度不足的问题。为解决上述问题,提出了一种由部件隐向量驱动的隐式三维重建方法,即构建部件的隐式场以最小化模型预测的整体形状目标点有符号距离值LGI-RIF(Reconstruction of Implicit Fields with Local and Global Integration),能从观测数据中重建几何形状。该方法在一个低维的潜在编码空间中训练神经网络并在解码器框架中联合优化,设计EFP、EFCS和R3DS这3个模块,在EFP模块中由设计的变分自编码器学习部件的特征向量分布,在EFCS模块中构建自动解码器学习整体形状的SDF隐式表达,在R3DS模块中重建整体三维形状。实验结果表明:LGI-RIF在ShapeNet和ModelNet 10数据集上的重建精度得到了进一步提升,在可视化重构中具有良好的视觉效果。
基金National High-tech Research and Development Pro-gram (2006AA04Z405)
文摘In order to deal with the issue of huge computational cost very well in direct numerical simulation, the traditional response surface method (RSM) as a classical regression algorithm is used to approximate a functional relationship between the state variable and basic variables in reliability design. The algorithm has treated successfully some problems of implicit performance function in reliability analysis. However, its theoretical basis of empirical risk minimization narrows its range of applications for...
基金Project supported by the National Natural Science Foundation of China (No.10572117)the National Astronautics Science Foundation of China (Nos.N3CH0502 and N5CH0001)Program for New Century Excellent Talent of Ministry of Education of China (No.NCET-05-0868)
文摘Support vector machine （SVM） was introduced to analyze the reliability of the implicit performance function, which is difficult to implement by the classical methods such as the first order reliability method （FORM） and the Monte Carlo simulation （MCS）. As a classification method where the underlying structural risk minimization inference rule is employed, SVM possesses excellent learning capacity with a small amount of information and good capability of generalization over the complete data. Hence, two approaches, i.e., SVM-based FORM and SVM-based MCS, were presented for the structural reliability analysis of the implicit limit state function. Compared to the conventional response surface method （RSM） and the artificial neural network （ANN）, which are widely used to replace the implicit state function for alleviating the computation cost, the more important advantages of SVM are that it can approximate the implicit function with higher precision and better generalization under the small amount of information and avoid the ＂curse of dimensionality＂. The SVM-based reliability approaches can approximate the actual performance function over the complete sampling data with the decreased number of the implicit performance function analysis （usually finite element analysis）, and the computational precision can satisfy the engineering requirement, which are demonstrated by illustrations.
文摘The key problem in the computation of fluid dynamics using fine boundary-fitted grids is how to improve the numerical stability and decrease the calculating quantity. To solve this problem, implicit schemes should be adopted since explicit schemes may bring about a great increase in computation quantity according to the Courant-FrledrichsLewy condition. Whereas the adoption of implicit schemes is difficult to be realized because of the existence of two partial derivatives of surface elevations with respect to variables of alternative direction coordinates in each momentum equation in non-rectangular coordinates. With an aim to design an implicit scheme in non-reetangular ccordinates in the present paper, new momentum equations with the contravariant components of velocity vector are derived based on the shallow water dynamic equations in generalized curvilinear coordinates. In each equation, the coefficients before the two detivatives of surface elevations have different orders of magnitude, i. e., the derivative with the larger ceefficient rnay play a more important role than that with the smaller one. With this advantage, the ADI scheme can then be easily employed to improve the numerical stability and decrease the calculating quantity. The calculation in a harbour and a channel in Macau nearshore area shows that the implicit model is effective in calculating current fields in small size areas.
