Sensitivity Analysis of Mathematical Models

IF 1.9 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Computation Pub Date : 2023-08-14 DOI:10.3390/computation11080159

A. Sysoev

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引用次数: 2

Abstract

The construction of a mathematical model of a complicated system is often associated with the evaluation of inputs’ (arguments, factors) influence on the output (response), the identification of important relationships between the variables used, and reduction of the model by decreasing the number of its inputs. These tasks are related to the problems of Sensitivity Analysis of mathematical models. The author proposes an alternative approach based on applying Analysis of Finite Fluctuations that uses the Lagrange mean value theorem to estimate the contribution of changes to the variables of a function to the output change. The article investigates the presented approach on an example of a class of fully connected neural network models. As a result of Sensitivity Analysis, a set of sensitivity measures for each input is obtained. For their averaging, it is proposed to use a point-and-interval estimation algorithm using Tukey’s weighted average. The comparison of the described method with the computation of Sobol’s indices is given; the consistency of the proposed method is shown. The computational robustness of the procedure for finding sensitivity measures of inputs is investigated. Numerical experiments are carried out on the neuraldat data set of the NeuralNetTools library of the R data processing language and on data of the healthcare services provided in the Lipetsk region.

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数学模型的敏感性分析

一个复杂系统的数学模型的构建通常与输入(参数、因素)对输出(响应)的影响的评估、所使用的变量之间的重要关系的识别以及通过减少输入的数量来减小模型有关。这些任务涉及到数学模型的敏感性分析问题。作者提出了一种基于有限波动分析的替代方法，该方法使用拉格朗日中值定理来估计函数变量变化对输出变化的贡献。本文以一类全连接神经网络模型为例，研究了所提出的方法。通过灵敏度分析，得到了每个输入的一组灵敏度度量。对于它们的平均，提出了一种基于Tukey加权平均的点区间估计算法。并将所描述的方法与Sobol指数的计算方法进行了比较;证明了所提方法的一致性。研究了寻找输入灵敏度测度过程的计算鲁棒性。在R数据处理语言的NeuralNetTools库的神经数据集和利佩茨克地区提供的医疗保健服务数据上进行了数值实验。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Computation Mathematics-Applied Mathematics

CiteScore

3.50

自引率

4.50%

发文量

201

审稿时长

8 weeks

期刊介绍： Computation a journal of computational science and engineering. Topics: computational biology, including, but not limited to: bioinformatics mathematical modeling, simulation and prediction of nucleic acid (DNA/RNA) and protein sequences, structure and functions mathematical modeling of pathways and genetic interactions neuroscience computation including neural modeling, brain theory and neural networks computational chemistry, including, but not limited to: new theories and methodology including their applications in molecular dynamics computation of electronic structure density functional theory designing and characterization of materials with computation method computation in engineering, including, but not limited to: new theories, methodology and the application of computational fluid dynamics (CFD) optimisation techniques and/or application of optimisation to multidisciplinary systems system identification and reduced order modelling of engineering systems parallel algorithms and high performance computing in engineering.