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Project Information
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In my geophysical work, I rely heavily upon a generalized inversion algorithm called Gauss-Newton optimization. The Gauss-Newton method minimizes objective functions that can be iteratively approximated by quadratics. This approach is particularly appropriate for least-squares inversions of moderately non-linear transforms. The package also contains code for conjugate-gradient and line-search optimizations. Over two decades I have implemented this package four times, in four different programming languages. Every feature of this package has been motivated by practical application. This particular Java version is only a few years old, but I have already used it for a dozen or more distinct inversion problems. I find no preexisting package so suitable for typical geophysical inversion problems. The abstraction is designed to minimize the burden of supporting new models, data, and transforms. Unlike many approaches, we will not be required to construct and invert large linear matrices. We only need to be able to perform transformations on specific models and datasets. The inversion algorithm need not know any of the implementation details of those models and transformations. For each new problem, I must implement two distinct Java interfaces. The data and model are be encapsulated by two implementations of the 'Vect' interface. The simulation to be inverted must be encapsulated by 'Transform' if non-linear, or by 'LinearTransform' if linear. Finally, the model that best explains a particular dataset is inverted by one of the 'GaussNewtonSolver.solve' methods. Any constraints or conditioning can be implemented with one of these interfaces. Bill Harlan |
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