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基于分级神经网络的柱形代数分解变元序选择
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作者 朱章鹏 陈长波 《计算机科学》 CSCD 北大核心 2020年第S02期106-110,138,共6页
柱形代数分解是广泛应用于求多项式系统实数解的一种计算方法。不同的变元序对其计算时间有显著影响。已有选序算法多基于启发式的经验算法,准确率不高。少数基于机器学习的方法使用的数据集较小,且基于复杂人工特征。文中在随机生成大... 柱形代数分解是广泛应用于求多项式系统实数解的一种计算方法。不同的变元序对其计算时间有显著影响。已有选序算法多基于启发式的经验算法,准确率不高。少数基于机器学习的方法使用的数据集较小,且基于复杂人工特征。文中在随机生成大量多项式系统与所有序计算时间标注的数据基础上,提出一类新的多项式显性表示特征和一种新的分级神经网络。首先根据最差序计算时间将数据集划分成4个不同计算难度的子集并分别建立预测最优序的分类模型,其次建立预测最长计算时间的回归模型,最后根据回归模型预测最长计算时间并据其自动选择相应难度分类模型预测最优变元序。实验结果表明,显性特征的性能优于复杂人工特征,且在困难问题上分级神经网络所预测最优序的性能约为经验选序算法的3倍。 展开更多
关键词 分级神经网络 柱形代数分解 变元序 回归 特征选择
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Numerical Simulation for Water Entry of a Wedge at Varying Speed by a High Order Boundary Element Method 被引量:6
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作者 Guoxiong Wu 《Journal of Marine Science and Application》 2012年第2期143-149,共7页
A high order boundary element method was developed for the complex velocity potential problem. The method ensures not only the continuity of the potential at the nodes of each element but also the velocity. It can be ... A high order boundary element method was developed for the complex velocity potential problem. The method ensures not only the continuity of the potential at the nodes of each element but also the velocity. It can be applied to a variety of velocity potential problems. The present paper, however, focused on its application to the problem of water entry of a wedge with varying speed. The continuity of the velocity achieved herein is particularly important for this kind of nonlinear free surface flow problem, because when the time stepping method is used, the free surface is updated through the velocity obtained at each node and the accuracy of the velocity is therefore crucial. Calculation was made for a case when the distance S that the wedge has travelled and time t follow the relationship s=Dtα, where D and α are constants, which is found to lead to a self similar flow field when the effect due to gravity is ignored. 展开更多
关键词 high order boundary element method complex velocity potential fluid/structure impact water entry
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Curling of New Concrete Pavement and Long-Term Performance
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作者 Daba S. Gedafa M. Hossain +2 位作者 Z. Q. Siddique K. Fredrichs D. Meggers 《Journal of Civil Engineering and Architecture》 2012年第2期121-130,共10页
Curling results from the temperature differential across the concrete slab thickness and may induce undue stresses in newly placed slab. This study deals with the finite element (FE) analysis of curling, curling str... Curling results from the temperature differential across the concrete slab thickness and may induce undue stresses in newly placed slab. This study deals with the finite element (FE) analysis of curling, curling stresses, field measurement of curling on a newly built jointed plain concrete pavement, and comparison of its long-term performance using both Mechanistic-Empirical Pavement Design Guide (MEPDG) and HIPERPAVII software. The FE analysis was performed with a software program, ANSYS. The test section was modeled as a three-layer system with 300 mm concrete slab, 100 mm treated drainable base, and 150 mm lime-treated subgrade. All layers were assumed to be linear elastic. Temperature data was collected at five different depth locations across the concrete slab with digital data loggers. Curling was measured on five different days with a simple setup. The effect of temperature nonlinearities across the slab thickness was also examined. The results show that both upward and downward curling increase as the temperature differential increases. The maximum stress resulting from the combined effect of curling and traffic loading due to positive temperature differential is higher than that due to the negative temperature differential of the same magnitude. Since temperature differential has a significant influence on curling, both curling and curling stresses can be mitigated at an early age with temperature control, namely via enhanced curing. Both MEPDG and HIPERPAVII showed approximately the same performance for the PCC thickness ranging from 215 mm to 300 mm for this project. Performance prediction from HIPERPAVII is very sensitive to the change in PCC thickness less than 230 mm whereas MEPDG prediction is not as sensitive to the thickness change as with HIPERPAV 1I. 展开更多
关键词 CURLING HIPERPAVII long-term performance MEPDG.
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基于机器学习的柱形代数分解变元择序 被引量:1
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作者 朱章鹏 陈长波 《系统科学与数学》 CSCD 北大核心 2020年第8期1492-1506,共15页
柱形代数分解(cylindrical algebraic decomposition,CAD)是计算实代数几何的基本工具之一,在很多领域都有重要应用.理论和实践表明不同的变元序对CAD的计算效率影响很大.已有的CAD的选序算法基本上是根据经验来选择,也有学者研究了用... 柱形代数分解(cylindrical algebraic decomposition,CAD)是计算实代数几何的基本工具之一,在很多领域都有重要应用.理论和实践表明不同的变元序对CAD的计算效率影响很大.已有的CAD的选序算法基本上是根据经验来选择,也有学者研究了用机器学习的方法来选择不同的经验选序算法.和已有方法不同,文章用机器学习的方法直接选择变元序.文章基于多项式组的图结构,提出了一组新的特征.实验表明利用这些特征训练出的多分类器预测最佳变元序的能力不仅明显优于随机择序,也优于Maple命令Suggest VariableOrder实现的传统启发式方法. 展开更多
关键词 变元序 机器学习 柱形代数分解 特征提取
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基于强化学习的柱形代数分解变元择序
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作者 荆瑞娟 钱铖镕 陈长波 《系统科学与数学》 2024年第9期2826-2849,共24页
柱形代数分解是半代数系统求解和实量词消去的基本工具.实际求解过程中,不同变元序的选择对柱形代数分解的效率影响重大.目前已有的启发式或机器学习择序的方法基本都建立在多项式系统的支撑集是影响变元序的决定因素这一隐含假设上.文... 柱形代数分解是半代数系统求解和实量词消去的基本工具.实际求解过程中,不同变元序的选择对柱形代数分解的效率影响重大.目前已有的启发式或机器学习择序的方法基本都建立在多项式系统的支撑集是影响变元序的决定因素这一隐含假设上.文章首先通过设计同支撑集变系数的实验对这一假设进行了检验,实验表明支撑集确实是影响最佳变元序的重要因素但并非唯一因素.针对同支撑集变系数的柱形代数分解最佳择序问题,文章设计了基于强化学习的择序方案,四变元的实验表明该方案可以突破已有方法只依赖支撑集选择最佳变元序准确率的上限.另外,针对多达二十万亿可选序系统的实验表明,该方案远优于传统的启发式方法.同已有的针对较少变元的监督学习择序方案相比,该强化学习方案克服了变元增多导致序数量组合爆炸时获得高质量标记数据的困难. 展开更多
关键词 半代数系统 柱形代数分解 变元序 强化学习 支撑集
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