Abstract
In the current study, a large-scale air pollution model is adopted, focusing on the Sobol’ approach for sensitivity analysis. In this paper we will use the advanced stochastic approach based on component by component construction methods. Optimized algorithms based on lattice rules have been designed and implemented, while their performance has been compared to the best available stochastic approaches, applied for multidimensional sensitivity analysis. Numerical results show a significant improvement over the current stochastic methods. The obtained results would have an important multi-sided role in the area of air pollution modeling.
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References
Baldeaux, J., Dick, J., Leobacher, G., Nuyens, D., Pillichshammer, F.: Efficient calculation of the worst-case error and (fast) component-by-component construction of higher order polynomial lattice rules. Numer. Algor. 59, 403–431 (2012)
Dimov, I.T.: Monte Carlo Methods for Applied Scientists, p. 291. World Scientific, Singapore (2008)
Kuo, F.Y., Nuyens, D.: Application of quasi-Monte Carlo methods to elliptic PDEs with random diffusion coefficients - a survey of analysis and implementation. Found. Comput. Math. 16, 1631–1696 (2016)
Saltelli, A., Tarantola, S., Campolongo, F., Ratto, M.: Sensitivity Analysis in Practice: A Guide to Assessing Scientific Models. Halsted Press, New York (2004)
Sobol, I.M.: Numerical Methods Monte Carlo. Nauka, Moscow (1973)
Sobol, I.M.: Sensitivity estimates for nonlinear mathematical models. Math. Modeling Comput. Experiment 1(4), 407–414 (1993)
Wang, Y., Hickernell, F.J.: An historical overview of lattice point sets. In: Fang, K.T., Niederreiter, H., Hickernell, F.J. (eds.) Monte Carlo and Quasi-Monte Carlo Methods 2000, pp. 158–167. Springer, Heidelberg (2002). https://doi.org/10.1007/978-3-642-56046-0_10
Zlatev, Z., Dimov, I.T., Georgiev, K.: Three-dimensional version of the Danish Eulerian model. Z. Angew. Math. Mech. 76(S4), 473–476 (1996)
Zlatev, Z., Dimov, I.T.: Computational and Numerical Challenges in Environmental Modelling. Elsevier, Amsterdam (2006)
Acknowledgements
Slavi Georgiev is supported by the Bulgarian National Science Fund (BNSF) under Project KP-06-M62/1 “Numerical deterministic, stochastic, machine and deep learning methods with applications in computational, quantitative, algorithmic finance, biomathematics, ecology and algebra” from 2022. Venelin Todorov is supported by BNSF under Project KP-06-N52/5 “Efficient methods for modeling, optimization and decision making” and BNSF under Project KP-06-N62/6 “Machine learning through physics-informed neural networks”. The work is also supported by BNSF under Bilateral Project KP-06-Russia/17 “New Highly Efficient Stochastic Simulation Methods and Applications”.
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Todorov, V., Georgiev, S., Dimov, I., Georgieva, R., Ostromsky, T. (2024). Improved Stochastic Lattice Methods for Large-Scale Air Pollution Model. In: Lirkov, I., Margenov, S. (eds) Large-Scale Scientific Computations. LSSC 2023. Lecture Notes in Computer Science, vol 13952. Springer, Cham. https://doi.org/10.1007/978-3-031-56208-2_37
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DOI: https://doi.org/10.1007/978-3-031-56208-2_37
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