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Advanced stochastic approaches for Sobol’ sensitivity indices evaluation

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Abstract

Sensitivity analysis is a modern promising technique for studying large systems such as ecological systems. The main idea of sensitivity analysis is to evaluate and predict (through computer simulations on large mathematical models) the measure of the sensitivity of the model’s output to the perturbations of some input parameters, and it is a technique for refining the mathematical model. The main problem in the sensitivity analysis is the evaluation of total sensitivity indices. The mathematical formulation of this problem is represented by a set of multidimensional integrals. In this work, some new stochastic approaches for evaluating Sobol’ sensitivity indices of the unified Danish Eulerian model have been presented. For the first time, a special type of digital nets and lattice rules are applied for multidimensional sensitivity analysis and their advantages are discussed. A comparison of accuracy of eight stochastic approaches for evaluating Sobol’ sensitivity indices is performed. The obtained results will be important and useful for the surveyed scientists (physicists, chemicals, meteorologists) to make a comparative classification of the input parameters with respect to their influence on the concentration of the pollutants of interest.

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Acknowledgements

Venelin Todorov is supported by the National Program—2020 “Young scientists and Postdoctoral candidates” of the Bulgarian Ministry of Education and Science. Stoyan Apostolov and Yuri Dimitrov are supported by the Bulgarian National Science Fund under Young Scientists Project KP-06-M32/2-17.12.2019 “Advanced Stochastic and Deterministic Approaches for Large-Scale Problems of Computational Mathematics.” The work is also partially supported by the National Scientific Program “Information and Communication Technologies for a Single Digital Market in Science, Education and Security (ICT in SES),” Contract No DO1–205/23.11.2018, financed by the Ministry of Education and Science in Bulgaria and by the Bulgarian National Science Fund under Project DN 12/5-2017 “Efficient Stochastic Methods and Algorithms for Large-Scale Problems.”

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Authors and Affiliations

  1. Information Modeling Department, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. Georgi Bonchev Str., Block 8, 1113, Sofia, Bulgaria

    Venelin Todorov

  2. Department of Parallel Algorithms, Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Block 25 A, 1113, Sofia, Bulgaria

    Venelin Todorov, Ivan Dimov, Tzvetan Ostromsky & Rayna Georgieva

  3. Faculty of Mathematics and Informatics, Sofia University, 1126, Sofia, Bulgaria

    Stoyan Apostolov

  4. University of Forestry, Sofia, Bulgaria

    Yuri Dimitrov

  5. Department of Environmental Science, Aarhus University, Roskilde, Denmark

    Zahari Zlatev

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  1. Venelin Todorov
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  2. Ivan Dimov
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Todorov, V., Dimov, I., Ostromsky, T. et al. Advanced stochastic approaches for Sobol’ sensitivity indices evaluation. Neural Comput & Applic 33, 1999–2014 (2021). https://doi.org/10.1007/s00521-020-05074-4

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