Efficient calculation of Jacobian and adjoint vector products in the wave propagational inverse problem using automatic differentiation
Wave propagational inverse problems arise in several applications including medical imaging and geophysical exploration. In these problems, one is interested in obtaining the parameters describing the medium from its response to excitations. The problems are characterized by their large size, and by the hyperbolic equation which models the physical phenomena. The inverse problems are often posed as a nonlinear data-fitting where the unknown parameters are found by minimizing the misfit between the predicted data and the actual data. In order to solve the problem numerically using a gradient-type approach, one must calculate the action of the Jacobian and its adjoint on a given vector. In this paper, the authors explore the use of automatic differentiation (AD) to develop codes that perform these calculations. They show that by exploiting structure at 2 scales, they can arrive at a very efficient code whose main components are produced by AD. In the first scale they exploit the time-stepping nature of the hyperbolic solver by using the Extended Jacobian framework. In the second (finer) scale, they exploit the finite difference stencil in order to make explicit use of the sparsity in the dependence of the output variables to the input variables. The main ideas in this work are illustrated with a simpler, one-dimensional version of the problem. Numerical results are given for both one- and two-dimensional problems. They present computational templates that can be used in conjunction with optimization packages to solve the inverse problem.
- Research Organization:
- Cornell Univ., Ithaca, NY (US)
- Sponsoring Organization:
- USDOE; National Science Foundation (NSF); US Department of the Air Force
- DOE Contract Number:
- FG02-94ER25225
- OSTI ID:
- 20014350
- Journal Information:
- Journal of Computational Physics, Vol. 157, Issue 1; Other Information: PBD: 1 Jan 2000; ISSN 0021-9991
- Country of Publication:
- United States
- Language:
- English
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