The terms “inverse problems” and “ill-posed have been steadily surely gaining popularity in modern science since the middle of 20th century. A little more than fifty years studying problems this kind shown that a great number from various branches classical mathematics (computational algebra, differential integral equations, partial functional analysis) can be classified as inverse or ill-posed, they are among most complicated ones (since unstable usually nonlinear). At same time, ill-posed...

Abstract The coefficient inverse problem for the two-dimensional wave equation is solved. We apply Gelfand–Levitan approach to transform nonlinear a family of linear integral equations. consider Monte Carlo method solving equation. obtain estimation solution in one specific point, due properties method. That allows be more effective terms span cost, compared with regular methods system. Results numerical simulations are presented.

Abstract The coefficient inverse problem for the acoustic equation is considered. We propose method reconstructing density based on N -approximation by finite system of one-dimensional problems and two-dimensional M. G. Krein approach. analogue approach applied to reduce non-linear a family linear integral equations. consider fast algorithm solving relevant system, using block-Toeplitz structure matrix. allows obtain solution whole equations only one system. Results numerical calculations...

Abstract. We consider the continuation problem from time-like surface for 2D Maxwell equation. The is formulated in an operator form . describe and justify gradient methods minimizing cost functional coefficient inverse problems. results of a computational experiment are presented.

We investigate inverse problems of finding unknown parameters mathematical models SEIR-HCD and SEIR-D COVID-19 spread with additional information about the number detected cases, mortality, self-isolation coefficient, tests performed for city Moscow Novosibirsk region since 23.03.2020. In population is divided into seven groups, in five groups similar characteristics transition probabilities depending on specific interest. An identifiability analysis made to reveal least sensitive as related...

Abstract Four simple mathematical models of pharmacokinetic, competition between immune and tumor cells, infectious disease tuberculosis epidemic are considered. An optimization approach for identification those based on gradient type methods is introduced. Inverse problems formulated in the form an operator equation then reduced to minimization corresponding misfit functionals. The adjoint used calculation gradients. A model cells considered numerically. results a numerical experiment demonstrated.

Abstract The paper considers an inverse problem and a direct for the Burgers equation in domain with movable boundaries. With help of additional condition, formula is obtained determining desired function from loaded solvability which we require condition on functions according to boundaries change. problems proved using priori estimates methods Faedo–Galerkin functional analysis.

Abstract In this paper, we revisit Linear Neural Networks (LNNs) with single-output neurons performing linear operations. The study focuses on constructing an optimal regularized weight matrix Q from training pairs <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mo stretchy="false">{</m:mo> <m:mi>G</m:mi> <m:mo>,</m:mo> <m:mi>H</m:mi> stretchy="false">}</m:mo> </m:mrow> </m:math> {\{G,H\}} , reformulating the LNNs framework as equations, and addressing it a inverse problem....

In this paper we apply the notion of quasi-solution to nonlinear inverse coefficient problems. Instead a compact set M use ball B(0, r) in which radius r occurred be sometimes regularization parameter. Moreover constant allows one estimate convergence rate for many well-known algorithms solving problems and decrease crucially number iterations.

Abstract The inverse problem for the acoustic equation is considered. We propose a method of reconstruction density approximating 2D by finite system one dimensional problems. analogy Gel'fand–Levitan–Krein established. formulated and short outline history development in this field are given Section 1. In 2 we consider equation. N-approximation obtained 3. numerical results presented 4.

Abstract. We investigate the continuation problem for elliptic equation. The is formulated in operator form . singular values of A are presented and analyzed Helmholtz Results numerical experiments presented.

Abstract An inverse problem of reconstructing the two-dimensional coefficient wave equation is solved by a stochastic projection method. We apply Gel'fand–Levitan approach to reduce nonlinear family linear integral equations. The method applied solve relevant system. analyze structure increase efficiency constructing an improved initial approximation. A smoothing spline used treat random errors has low cost and memory requirements. Results numerical calculations are presented.

Abstract The problem of identification unknown epidemiological parameters (contagiosity, the initial number infected individuals, probability being tested) an agent-based model COVID-19 spread in Novosibirsk region is solved and analyzed. first stage modeling involves data analysis based on machine learning approach that allows one to determine correlated datasets performed PCR tests daily diagnoses detect some features (seasonality, stationarity, correlation) be used for modeling. At second...

We consider an ill-posed initial boundary value problem for the Helmholtz equation. This is reduced to inverse continuation prove well-posedness of direct and obtain a stability estimate its solution. solve numerically using Tikhonov regularization, Godunov approach, Landweber iteration. Comparative analysis these methods presented.

The eleventh international annual scientific school-conference "Theory and numerical methods for solving inverse ill-posed problems" will be held in August 26-September 4, 2019.It organized by Novosibirsk State University Institute of Computational Mathematics Mathematical Geophysics the SB RAS.The first ten school-conferences, from 2009 to 2018, showed relevance significance chosen subject.Over past years, researchers, graduate students undergraduates Russia, Belarus, Ukraine, Kazakhstan,...