基于深度学习的智能全局灵敏度分析

doi:10.16183/j.cnki.jsjtu.2021.191

摘要/Abstract

摘要：

提出一种将深度学习与灵敏度分析结合的端到端方法, 对深度模型的结构和激活函数进行特殊设计以适应后续灵敏度的计算,深度模型训练的同时对保存的权重信息进行反向传播计算灵敏度.在波士顿房价数据集、航迹融合数据集和G函数上的实验结果表明,所提方法相比于Sobol’法等经典方法在参数分布不均匀时准确性更高, 具备更强的鲁棒性, 相比于使用传统神经网络的方法准确性更高.此外,通过实验验证了基于深度学习模型的样本参数灵敏度可以优化模型的输出结果.

关键词: 卷积神经网络, Inception模块, 灵敏度分析, Sobol’ 方法, 非线性系统分析, 深度学习

Abstract:

This paper proposes an end-to-end method that combines deep learning and sensitivity analysis, which can perform gradient back propagation calculation sensitivity on the saved weight information while training the model. The structure and activation function of the depth model are specially designed to adapt to the subsequent sensitivity calculation. The experimental results conducted on a Boston house prices dataset, a track information fusion dataset, and the G function show that the proposed method is more accurate than classical methods such as Sobol’ method when the parameter distribution is uneven, and has a stronger robustness. Compared with the traditional neural network method, the accuracy of the proposed method is higher. The experiment proves that the sample parameter sensitivity obtained by the deep learning model can be used to optimize the model output.

Key words: convolutional neural network, Inception module, sensitivity analysis, Sobol’ method, nonlinear system analysis, deep learning

中图分类号:

TB112

吴庶宸, 戚宗锋, 李建勋. 基于深度学习的智能全局灵敏度分析[J]. 上海交通大学学报, 2022, 56(7): 840-849.

WU Shuchen, QI Zongfeng, LI Jianxun. Intelligent Global Sensitivity Analysis Based on Deep Learning[J]. Journal of Shanghai Jiao Tong University, 2022, 56(7): 840-849.

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模型	测试集 MSE	测试集 MAE	测试集平均误差率/%
NN	0.268	2.21	13.50
CNN	0.095	1.62	9.90
SInception-CNN	0.072	1.54	9.41

参数	SInception-CNN		参数	Sobol’法
参数	正常	加入脏样本	参数	正常	加入脏样本
房屋总面积	61.52(1)	64.07(1)	房屋总面积	64.25(1)	93.64(1)
地上居住面积	5.22(2)	5.49(2)	房屋一层面积	10.52(2)	0.13(8)
杂项物品总价值	5.05(3)	4.37(3)	地下室已装修面积	9.51(3)	0.55(5)
地下室已装修面积	4.47(4)	3.96(4)	杂项物品总价值	3.96(4)	1.15(3)
地下室未装修面积	4.36(5)	3.88(5)	车库面积	3.05(5)	0.12(9)

特征	定义
CRIM	城镇人均犯罪率
ZN	占地2322.576平方米以上住宅用地比例
INDUX	每个城镇工业用地的比例
CHAS	查尔斯河(如果临近河流则为1;否则为0)
NOX	一氧化氮浓度
RM	住宅平均房间数
AGE	1940年建造的房屋比例
DIS	与5个就业中心的距离加权和
RAD	公路通达性
TAX	资产税率
PTRATIO	师生比例
B	黑人比例
LSTAT	低收入人口比例