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12the sufficient conditions for the distinguishability of various substances [3]. Based on tabular data [4], calcula-
tions were made for a number of specific groups of chemical elements.
This work was supported by the Russian Foundation for Basic Research (project no. 20-01-00173).
References
1. Godunov S.K., Antonov A.G., Kiriluyk O.P., Kostin V.I. Guaranteed accuracy of solving systems of linear equations in
Euclidean spaces, Novosibirsk, Nauka, 1988, (in Russian).
2. Forsythe G.E., Malcolm M.A., Moler C.B. Computer methods for mathematical computations, Prentice-Hall, Inc.
Englewood Cliffs, N.J. 07632, 1977.
3. Nazarov V.G. Estimation of the Calculation Accuracy in the Problem of Partial Identification of a Substance // J. of
Applied and Industrial Mathematics, 2020. 14(3), pp. 555-565.
4. Berger M.J., Hubbell J.H., Seltzer S.M., Chang J., Coursey J.S., Sukumar R., Zucker D.S. XCOM: Photon Cross Section
Database, National Institute of Standards and Technology, Gaithersburg, 2005, URL: http://www.physics.nist.gov/xcom.
Optimization of solution of inverse problem for stochastic differential equation
A. V. Neverov1, O. I. Krivorotko1,2
1Novosibirsk State University
2Institute of Computational Mathematics and Mathematical Geophysics SB RAS
Email: a.neverov@g.nsu.ru
DOI 10.24412/cl-35065-2021-1-03-04
The problem of drift and volatility parameters identification in stochastic differential equations (SDEs) us-
ing additional measurement of single trajectory of stochastic process is investigated. The classical way for solv-
ing such a problem is to reduce it to a Fokker-Planck equation [1] and minimize a data fidelity functional, that
is unstable. For higher-dimensional systems of SDEs, the numerical solution of the Fokker-Planck equations
becomes infeasible.
We propose regularized Landweber iteration algorithm [2] with fidelity functional based on mathematical
expectations, for easier parallelization of solution. Parameters are implemented in solution-dependent form,
for implicit time-dependency, with Fourier series for reducing number of variables. In addition to that adjoint
problem is deterministic. We conduct this process on synthetic data for validation of an algorithm and regular-
ization for variety of input data with Tikhonov regularization.
This work was supported by the Russian Science Foundation (project no. 18-71-10044).
References
1. Risken H.: The Fokker-Planck equation. Methods of solution and applications. Springer Series in Synergetics,
Springer-Verlag, 1989.
2. Kaltenbacher B., Schopfer F., and Schuster T.: Iterative methods for non-linear ill-posed problems in Banach spac-
es: convergence and applications to parameter identification problems. Inverse Problems, 2009.
Numerical solution of inverse problem for acoustic equation, based on a modified version
of GLK-approach
N. S. Novikov
Institute of Computational Mathematics and Mathematical Geophysics SB RAS
Novosibirsk State University
Email: novikov-1989@yandex.ru
DOI 10.24412/cl-35065-2021-1-02-05
In this talk we consider the coefficient inverse problems for the acoustic equation in 1D and 2D cases
[1�3]. We propose the new version of the Gelfand � Levitan � Krein approach to reduce the non-linear inverse
problem to a set of linear integral equations. We study the possibility to use the method in case of general
time form of the sounding wave. In 2D case we also consider the modification of the method that uses the da-
ta, obtained by the areal data collection system. The results of numerical experiments are presented.
This work has been supported by the Russian Science Foundation under grant 20-71-00128 "Development of new al-
gorithms for parameters identification of geophysics based on the direct methods of data processing".
References
1. Kabanikhin, S.I., Novikov, N.S., Oseledets, I.V., Shishlenin, M.A., Fast Toeplitz linear system inversion for solving
two-dimensional acoustic inverse problem, Journal of Inverse and Ill-Posed Problems, 2015, v. 23 N. 5. P. 687�700.
2. Kabanikhin, S.I., Sabelfeld, K.K., Novikov, N.S., Shishlenin, M.A., Numerical solution of the multidimensional
Gelfand-Levitan equation, Journal of Inverse and Ill-Posed Problems, 2015, v. 23. N. 5. P. 439-450.
3. Kabanikhin, S.I., Sabelfeld, K.K., Novikov, N.S., Shishlenin, M.A., Numerical solution of an inverse problem of
coefficient recovering for a wave equation by a stochastic projection methods, Monte Carlo Methods and Applications,
2015. V. 21, N. 3. P. 189�203.
Mean field games for modeling of disease propagation
V. Petrakova1, O. Krivorotko2,3
1Institute of Computational Modelling SB RAS, Krasnoyarsk
2Institute of Computational Mathematics and Mathematical Geophysics SB RAS
3Novosibirsk State University
Email: vika-svetlakova@yandex.ru
DOI 10.24412/cl-35065-2021-1-03-05
The mean field game (MFG) that describes the control of a population with a large number of interacting
agents [1] is numerically investigated. MFG is based on Kolmogorov (Fokker � Planck) equations that charac-
terize the distributions of agents in four groups (susceptible, infected; recovered and cross-immune people)
and system of Hamilton-Jacobi-Bellman equations that describes the optimal strategy of isolation: if a person
is not infected and the number of non-isolating people in population is arising, person's profit decreases to
comply with the restrictions. Otherwise, if a person is infected, then he is inclined to comply with restrictions.
The optimality conditions are derived. The scenarios of COVID-19 propagation in Siberia depend on restrictions
[2] are modelled and discussed.
This work is supported by the Russian Science Foundation (grant no. 18-71-10044).
References
1. J.-M. Lasry and P.-L. Lions. Mean field games. Jpn. J. Math. 2007. V. 2, N. 1. P. 229-260.
2. O.I. Krivorotko, S.I. Kabanikhin, N.Yu. Zyatkov, et al. Mathematical modeling and forecasting of COVID-19 in Mos-
cow and Novosibirsk region. Numerical Analysis and Applications. 2020. V. 13, N. 4. P. 332-348.
On the singular value decomposition of the ray transforms operators acting on 2D tensor fields
A. P. Polyakova, I. E. Svetov
Sobolev Institute of Mathematics SB RAS
Email: apolyakova@math.nsc.ru
DOI 10.24412/cl-35065-2021-1-02-06
We consider the problem of the 2D m-tensor tomography. Namely, it is necessary to reconstruct a 2D
symmetric m-tensor field by values of its ray transforms. We propose to solve the problem with usage of the
