We develop a unified model, known as MgNet, that simultaneously recovers some convolutional neural networks (CNN) for image classification and multigrid (MG) methods for solving discretized partial differential equati...We develop a unified model, known as MgNet, that simultaneously recovers some convolutional neural networks (CNN) for image classification and multigrid (MG) methods for solving discretized partial differential equations (PDEs). This model is based on close connections that we have observed and uncovered between the CNN and MG methodologies. For example, pooling operation and feature extraction in CNN correspond directly to restriction operation and iterative smoothers in MG, respectively. As the solution space is often the dual of the data space in PDEs, the analogous concept of feature space and data space (which are dual to each other) is introduced in CNN. With such connections and new concept in the unified model, the function of various convolution operations and pooling used in CNN can be better understood. As a result, modified CNN models (with fewer weights and hyperparameters) are developed that exhibit competitive and sometimes better performance in comparison with existing CNN models when applied to both CIFAR-10 and CIFAR-100 data sets.展开更多
针对联合作战指挥体系效能评估面临的2个难点,即如何对指挥体系这个复杂巨系统进行建模分析,以及如何解决效能评估过程中遇到的评估指标类型多样和评估信息不完全等问题。首先,借助体系结构方法在复杂系统建模方面的优势,运用统一架构框...针对联合作战指挥体系效能评估面临的2个难点,即如何对指挥体系这个复杂巨系统进行建模分析,以及如何解决效能评估过程中遇到的评估指标类型多样和评估信息不完全等问题。首先,借助体系结构方法在复杂系统建模方面的优势,运用统一架构框架(Unified Architecture Framework,UAF)对指挥体系进行建模,以UAF视图模型为基础构建了评估指标体系;然后,利用基于证据推理算法的信度规则库推理方法(belief Rule-base Inference Methodology using the Evidential Reasoning,RIMER),通过综合专家经验、相关历史知识和仿真结果等信息构建了效能评估信度规则库,将不同类型的不确定性指标数据转换为信度结构来计算指挥体系的效能水平;最后,通过示例验证了方法的有效性。展开更多
基金supported by the Elite Program of Computational and Applied Mathematics for PhD Candidates of Peking Universitysupported in part by the National Science Foundation of USA (Grant No. DMS-1819157)+2 种基金the US Department of Energy Office of ScienceOffice of Advanced Scientific Computing ResearchApplied Mathematics Program (Grant No. DE-SC0014400)
文摘We develop a unified model, known as MgNet, that simultaneously recovers some convolutional neural networks (CNN) for image classification and multigrid (MG) methods for solving discretized partial differential equations (PDEs). This model is based on close connections that we have observed and uncovered between the CNN and MG methodologies. For example, pooling operation and feature extraction in CNN correspond directly to restriction operation and iterative smoothers in MG, respectively. As the solution space is often the dual of the data space in PDEs, the analogous concept of feature space and data space (which are dual to each other) is introduced in CNN. With such connections and new concept in the unified model, the function of various convolution operations and pooling used in CNN can be better understood. As a result, modified CNN models (with fewer weights and hyperparameters) are developed that exhibit competitive and sometimes better performance in comparison with existing CNN models when applied to both CIFAR-10 and CIFAR-100 data sets.
文摘针对联合作战指挥体系效能评估面临的2个难点,即如何对指挥体系这个复杂巨系统进行建模分析,以及如何解决效能评估过程中遇到的评估指标类型多样和评估信息不完全等问题。首先,借助体系结构方法在复杂系统建模方面的优势,运用统一架构框架(Unified Architecture Framework,UAF)对指挥体系进行建模,以UAF视图模型为基础构建了评估指标体系;然后,利用基于证据推理算法的信度规则库推理方法(belief Rule-base Inference Methodology using the Evidential Reasoning,RIMER),通过综合专家经验、相关历史知识和仿真结果等信息构建了效能评估信度规则库,将不同类型的不确定性指标数据转换为信度结构来计算指挥体系的效能水平;最后,通过示例验证了方法的有效性。
