Standard

A Modification of gradient descent method for solving coefficient inverse problem for acoustics equations. / Klyuchinskiy, Dmitriy; Novikov, Nikita; Shishlenin, Maxim.

In: Computation, Vol. 8, No. 3, 73, 01.09.2020.

Research output: Contribution to journal › Article › peer-review

Harvard

Klyuchinskiy, D, Novikov, N & Shishlenin, M 2020, 'A Modification of gradient descent method for solving coefficient inverse problem for acoustics equations', Computation, vol. 8, no. 3, 73. https://doi.org/10.3390/COMPUTATION8030073

APA

Klyuchinskiy, D., Novikov, N., & Shishlenin, M. (2020). A Modification of gradient descent method for solving coefficient inverse problem for acoustics equations. Computation, 8(3), [73]. https://doi.org/10.3390/COMPUTATION8030073

Vancouver

Klyuchinskiy D, Novikov N, Shishlenin M. A Modification of gradient descent method for solving coefficient inverse problem for acoustics equations. Computation. 2020 Sept 1;8(3):73. doi: 10.3390/COMPUTATION8030073

Author

Klyuchinskiy, Dmitriy ; Novikov, Nikita ; Shishlenin, Maxim. / A Modification of gradient descent method for solving coefficient inverse problem for acoustics equations. In: Computation. 2020 ; Vol. 8, No. 3.

BibTeX

@article{9610022bd29f4aa4a1bcda527bf2f9a6,
title = "A Modification of gradient descent method for solving coefficient inverse problem for acoustics equations",
abstract = "We investigate the mathematical model of the 2D acoustic waves propagation in a heterogeneous domain. The hyperbolic first order system of partial differential equations is considered and solved by the Godunov method of the first order of approximation. This is a direct problem with appropriate initial and boundary conditions. We solve the coefficient inverse problem (IP) of recovering density. IP is reduced to an optimization problem, which is solved by the gradient descent method. The quality of the IP solution highly depends on the quantity of IP data and positions of receivers. We introduce a new approach for computing a gradient in the descent method in order to use as much IP data as possible on each iteration of descent.",
keywords = "Acoustics, First-order hyperbolic system, Godunov method, Gradient descent method, Inverse problem, Tomography, first-order hyperbolic system, inverse problem, HYPERBOLIC SYSTEMS, RECONSTRUCTION, ALGORITHM, SPATIAL DISTRIBUTIONS, NUMERICAL-SOLUTION, REGULARITY, tomography, TRAVEL-TIME TOMOGRAPHY, acoustics, ABSORPTION, gradient descent method, SOUND-VELOCITY, ULTRASOUND TOMOGRAPHY",
author = "Dmitriy Klyuchinskiy and Nikita Novikov and Maxim Shishlenin",
year = "2020",
month = sep,
day = "1",
doi = "10.3390/COMPUTATION8030073",
language = "English",
volume = "8",
journal = "Computation",
issn = "2079-3197",
publisher = "Multidisciplinary Digital Publishing Institute (MDPI)",
number = "3",

}

RIS

TY - JOUR

T1 - A Modification of gradient descent method for solving coefficient inverse problem for acoustics equations

AU - Klyuchinskiy, Dmitriy

AU - Novikov, Nikita

AU - Shishlenin, Maxim

PY - 2020/9/1

Y1 - 2020/9/1

N2 - We investigate the mathematical model of the 2D acoustic waves propagation in a heterogeneous domain. The hyperbolic first order system of partial differential equations is considered and solved by the Godunov method of the first order of approximation. This is a direct problem with appropriate initial and boundary conditions. We solve the coefficient inverse problem (IP) of recovering density. IP is reduced to an optimization problem, which is solved by the gradient descent method. The quality of the IP solution highly depends on the quantity of IP data and positions of receivers. We introduce a new approach for computing a gradient in the descent method in order to use as much IP data as possible on each iteration of descent.

AB - We investigate the mathematical model of the 2D acoustic waves propagation in a heterogeneous domain. The hyperbolic first order system of partial differential equations is considered and solved by the Godunov method of the first order of approximation. This is a direct problem with appropriate initial and boundary conditions. We solve the coefficient inverse problem (IP) of recovering density. IP is reduced to an optimization problem, which is solved by the gradient descent method. The quality of the IP solution highly depends on the quantity of IP data and positions of receivers. We introduce a new approach for computing a gradient in the descent method in order to use as much IP data as possible on each iteration of descent.

KW - Acoustics

KW - First-order hyperbolic system

KW - Godunov method

KW - Gradient descent method

KW - Inverse problem

KW - Tomography

KW - first-order hyperbolic system

KW - inverse problem

KW - HYPERBOLIC SYSTEMS

KW - RECONSTRUCTION

KW - ALGORITHM

KW - SPATIAL DISTRIBUTIONS

KW - NUMERICAL-SOLUTION

KW - REGULARITY

KW - tomography

KW - TRAVEL-TIME TOMOGRAPHY

KW - acoustics

KW - ABSORPTION

KW - gradient descent method

KW - SOUND-VELOCITY

KW - ULTRASOUND TOMOGRAPHY

UR - http://www.scopus.com/inward/record.url?scp=85090595430&partnerID=8YFLogxK

U2 - 10.3390/COMPUTATION8030073

DO - 10.3390/COMPUTATION8030073

M3 - Article

AN - SCOPUS:85090595430

VL - 8

JO - Computation

JF - Computation

SN - 2079-3197

IS - 3

M1 - 73

ER -

ID: 25292656