Abstract:
The algorithms for solving the inverse source problem for the production–destruction type systems of nonlinear ordinary differential equations with measurement data in the form of time series are presented. The sensitivity operator and its discrete analogue on the basis of adjoint equations are constructed. This operator binds the perturbations in the unknown parameters of the model to those of the measured values. The operator allows one to construct a family of quasi-linear operator equations linking the required unknown parameters and the data of the inverse problem. The Newton–Kantorovich type method with right-hand side rr-pseudoinverse matrices is used to solve the equations. The algorithm is applied to solving the inverse source problem for the atmospheric impurities transformation model.
Key words:
inverse source problem, big data, Newton–Kantorovich method, adjoint equations, sensitivity operator, rr-pseudoinverse matrix, right inverse.
This work was supported by the Russian Science Foundation (project no. 17-71-10184 for the
development of algorithms and their study) and by the Ministry of Education and Science of the
Russian Federation (project no. 4.1.3, joint laboratories of NSU–NSC SB RAS for the vectorization
and optimization of the software).
Citation:
A. V. Penenko, “The Newton–Kantorovich method in inverse source problems for production-destruction models with time series-type measurement data”, Sib. Zh. Vychisl. Mat., 22:1 (2019), 57–79; Num. Anal. Appl., 12:1 (2019), 51–69
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\by A.~V.~Penenko
\paper The Newton--Kantorovich method in inverse source problems for production-destruction models with time series-type measurement data
\jour Sib. Zh. Vychisl. Mat.
\yr 2019
\vol 22
\issue 1
\pages 57--79
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\crossref{https://doi.org/10.15372/SJNM20190105}
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\jour Num. Anal. Appl.
\yr 2019
\vol 12
\issue 1
\pages 51--69
\crossref{https://doi.org/10.1134/S1995423919010051}
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Linking options:
https://www.mathnet.ru/eng/sjvm701
https://www.mathnet.ru/eng/sjvm/v22/i1/p57
This publication is cited in the following 13 articles:
Gurami Tsitsiashvili, Alexey Gudimenko, Marina Osipova, “Fast Method for Estimating the Parameters of Partial Differential Equations from Inaccurate Observations”, Mathematics, 11:22 (2023), 4586
Gurami Tsitsiashvili, Marina Osipova, Yury Kharchenko, “Estimating the Coefficients of a System of Ordinary Differential Equations Based on Inaccurate Observations”, Mathematics, 10:3 (2022), 502
Alexey Penenko, Evgeny Rusin, “Parallel Implementation of a Sensitivity Operator-Based Source Identification Algorithm for Distributed Memory Computers”, Mathematics, 10:23 (2022), 4522
A. Penenko, V. Penenko, E. Tsvetova, A. Gochakov, E. Pyanova, V. Konopleva, “Sensitivity operator framework for analyzing heterogeneous air quality monitoring systems”, Atmosphere, 12:12 (2021), 1697
A. V. Penenko, Zh. S. Mukatova, A. B. Salimova, “Numerical study of the coefficient identification algorithm based on ensembles of adjoint problem solutions for a production-destruction model”, Int. J. Nonlinear Sci. Numer. Simul., 22:5 (2021), 581–592
G. Gallo, A. Isoldi, D. Del Gatto, R. Savino, A. Capozzoli, C. Curcio, A. Liseno, “Numerical aspects of particle-in-cell simulations for plasma-motion modeling of electric thrusters”, Aerospace, 8:5 (2021), 138
A. Penenko, “Convergence analysis of the adjoint ensemble method in inverse source problems for advection-diffusion-reaction models with image-type measurements”, Inverse Probl. Imaging, 14:5 (2020), 757–782
A. V. Penenko, A. B. Salimova, “Source indentification for the Smoluchowski equation
using an ensemble of the adjoint equation solutions”, Num. Anal. Appl., 13:2 (2020), 152–164
Alexey Penenko, Ulyana Zubairova, Alexander Bobrovskikh, Alexey Doroshkov, 2020 Cognitive Sciences, Genomics and Bioinformatics (CSGB), 2020, 14
Alexey Penenko, Alexander Gochakov, Vladimir Penenko, “Algorithms based on sensitivity operators for analyzing and solving inverse modeling problems of transport and transformation of atmospheric pollutants”, IOP Conf. Ser.: Earth Environ. Sci., 611:1 (2020), 012032
Penenko A., Mukatova Zh., Salimova A., “Numerical Solution of the Coefficient Inverse Problem For a Production-Destruction Model With Various Adjoint Ensemble Designs”, 2019 15Th International Asian School-Seminar Optimization Problems of Complex Systems (Opcs 2019), IEEE, 2019, 135–139
A V Penenko, Zh S Mukatova, A B Salimova, “Numerical analysis of an inverse coefficient problem for a chemical transformation model”, IOP Conf. Ser.: Earth Environ. Sci., 386:1 (2019), 012041
Alexey Penenko, Zhadyra Mukatova, Akzhan Salimova, 2019 15th International Asian School-Seminar Optimization Problems of Complex Systems (OPCS), 2019, 135
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