«Automation and Informatization of the fuel and energy complex»

Determination of the initial approximation in the inverse coefficient problem for evolutionary equations by the method of automatic differentiation

UDC: 519.63
DOI: -

Authors:

¹ National University of Oil and Gas "Gubkin University", Moscow, Russia

Keywords: inverse coefficient problems, numerical optimization, initial approximation guess, wave equation, finite differences method, Marmousi2 velocity section model

Annotation:

The authors of the article propose an approach to finding an initial approximation for the numerical solution of the inverse coefficient problem for an evolutionary equation with stationary coefficients. The results are demonstrated using a scalar inhomogeneous wave equation with a variable coefficient in one and two dimensions. Discretization is carried out using the finite differences method (FDM). The coefficient to be identified is represented in parametric form and determined using an iterative gradient optimization algorithm. At each step of the algorithm, the gradient is calculated using automatic differentiation over a single time layer of the explicit finite-difference scheme. The problem formulation when the wave field is known within the solution domain is also considered by the authors. It allows calculating the gradient for any time layer individually, regardless of the previous layers. The advantages and limitations of the proposed approach are also analyzed. The influence of regularization, noise, and filtering using the Savitsky – Golay method on the obtained results is demonstrated by several examples. The synthetic Marmusi2 model was used in one of the considered examples.

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