Efficient calculation of Jacobian and adjoint vector products in the wave propagational inverse problem using automatic differentiation
type: Item
instance of: scholarly article
title: Efficient calculation of Jacobian and adjoint vector products in the wave propagational inverse problem using automatic differentiation
zbMATH Open document ID: 0947.65104
author: Fadil Santosa
author: Arun Verma
author: Thomas F. Coleman
published in: Journal of Computational Physics
publication date: 2000-11-12T00:00:00Z
full work available at URL: http://purl.umn.edu/3236
review text: The paper deals with a type of inverse problems, also called identification problems, which consist in finding information on an unknown medium, being known a generated incident disturbance and the corresponding response. The latter has the form of reflected and refracted waves, produced by incident waves which travel in the unknown medium, and are collected by receivers. These nonlinear problems are very large. The number of unknowns and equations could be in the range \(10^3\sim 10^6\), so one cannot compute and store the entire Jacobian. They are posed in terms of optimization problems, solved by means of nonlinear least squares or some other procedure. The purpose of this article is to demonstrate the use of an extended Jacobian framework together with an exploitation of a stencil in Jacobian and adjoint calculations. Automatic differentiation (AD) is applied at the stencil level, and the resulting subprograms fit well within the extended Jacobian framework. The paper contains a description of AD, and an introduction to the inverse problem for acoustic waves. A section is devoted to review the extended Jacobian framework and to show how to exploit the underlying problem structure. Under the title ``Exploiting the stencil structure'', the authors present a section where the basic algorithm of the work is derived. They point out that the \(j\)th component of the finite difference equation \({\mathbf u}^{k+ 1}= F({\mathbf c},{\mathbf u}^k,{\mathbf u}^{k- 1})\), \({\mathbf u}^{-1}={\mathbf u}^0= \mathbf{0}\), reveals that the dependence of \({\mathbf u}^{k+ 1}\) on its vector variables is very sparse. The efficiency of the code is given by the fact that the time-step function is only based on three scalar functions depending on 2, 4 and 5 variables, respectively. The problem of that the derivative and the adjoint codes are slightly more complicated to assemble, is discussed in this section. An extension of the 2-D problem is investigated in the case when the receive…
Mathematics Subject Classification ID: 65M32
Mathematics Subject Classification ID: 65D25
Mathematics Subject Classification ID: 35L05
Mathematics Subject Classification ID: 35R30
Mathematics Subject Classification ID: 65M06
zbMATH DE Number: 1422638
zbMATH Keywords: wave propagation equation
zbMATH Keywords: numerical examples
zbMATH Keywords: automatic differentiation
zbMATH Keywords: inverse problems
zbMATH Keywords: identification problems
zbMATH Keywords: nonlinear problems
zbMATH Keywords: nonlinear least-squares
zbMATH Keywords: acoustic waves
zbMATH Keywords: finite difference equation
reviewed by: J. Illán
describes a project that uses: ADOL-C
describes a project that uses: TAMC
MaRDI profile type: Publication
OpenAlex ID: W1967903243
cites work: Q4341142
cites work: The Efficient Computation of Sparse Jacobian Matrices Using Automatic Differentiation
cites work: Q3840107
cites work: Q3125548
cites work: Absorbing Boundary Conditions for the Numerical Simulation of Waves
cites work: Some bounds on the complexity of gradients, Jacobians, and Hessians
cites work: Algorithm 755: ADOL-C
cites work: Computation of the Hessian for least-squares solutions of inverse problems of reflection seismology
cites work: Q3997001
DOI: 10.1006/JCPH.1999.6373
description: scientific article; zbMATH DE number 1422638