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報告題目： On sensitivity analysis by factors of mathematical models

報告時間：2024年4月23日（星期二）15:00--17:00

報告地點：理學院B315

主辦單位：理學院

報告人：Anton Sysoev

報告人簡介：

Anton Sysoev received the degree in Applied Mathematics in 2011 in Lipetsk State Technical University (diploma with honor). In 2014，he made his promotion as a Candidate of Technical Sciences with the thesis “Modeling and optimizing systems of variable structure using methods of Idempotent Mathematics and Analysis of Finite Fluctuations”. His scientific fields of interest are connected with mathematical modeling of distributed systems, technological processes and social and economic systems. Currently he specializes in Sensitivity Analysis of complicated mathematical structures.

報告內容簡介：

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. It is proposed 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 study 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.