We consider the problem of locating small openings inside the domain of definition of elliptic equation using as the observation data the values of finite number of integral functionals. Application of neural networks requires a great number of training sets. The approximation of these functionals by means of topological derivative allows to generate training data very quickly. The results of computations for 2D examples show, that the method allows to determine an approximation of the global solution to the inverse problem, sufficiently closed to the exact solution. © Springer-Verlag Berlin Heidelberg 2005.
CITATION STYLE
Jackowska-Strumiłło, L., Sokołowski, J., & Zochowski, A. (2005). Topological derivative and training neural networks for inverse problems. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 3697 LNCS, pp. 391–396). https://doi.org/10.1007/11550907_62
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