{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,12]],"date-time":"2025-02-12T23:40:20Z","timestamp":1739403620489,"version":"3.37.0"},"publisher-location":"Berlin, Heidelberg","reference-count":13,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783642048012"},{"type":"electronic","value":"9783642048029"}],"license":[{"start":{"date-parts":[[2009,1,1]],"date-time":"2009-01-01T00:00:00Z","timestamp":1230768000000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2009]]},"DOI":"10.1007\/978-3-642-04802-9_14","type":"book-chapter","created":{"date-parts":[[2009,10,27]],"date-time":"2009-10-27T14:32:56Z","timestamp":1256653976000},"page":"268-281","source":"Crossref","is-referenced-by-count":0,"title":["Applications of Topological Derivatives and Neural Networks for Inverse Problems"],"prefix":"10.1007","author":[{"given":"Marta","family":"Grzanek","sequence":"first","affiliation":[]},{"given":"Katarzyna","family":"Szulc","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"14_CR1","doi-asserted-by":"publisher","first-page":"930","DOI":"10.1109\/18.256500","volume":"39","author":"A.R. Baron","year":"1993","unstructured":"Baron, A.R.: Universal approximation bounds for superpositions of a sigmoidal function. IEEE Transactions on Information Theory\u00a039, 930\u2013945 (1993)","journal-title":"IEEE Transactions on Information Theory"},{"issue":"6","key":"14_CR2","doi-asserted-by":"publisher","first-page":"989","DOI":"10.1109\/72.329697","volume":"5","author":"M. Hagan","year":"1994","unstructured":"Hagan, M., Menhaj, M.: Training feedforward networks with the Marquardt algorithm. IEEE Trans. on Neural Networks\u00a05(6), 989\u2013993 (1994)","journal-title":"IEEE Trans. on Neural Networks"},{"key":"14_CR3","doi-asserted-by":"publisher","first-page":"231","DOI":"10.1023\/A:1020528902875","volume":"23","author":"L. Jackowska-Strumillo","year":"2002","unstructured":"Jackowska-Strumillo, L., Soko\u0142owski, J., \u017bochowski, A., Henrot, A.: On Numerical Solution of Shape Inverse Problems. Computational Optimization and Applications\u00a023, 231\u2013255 (2002)","journal-title":"Computational Optimization and Applications"},{"unstructured":"Mazja, W.G., Nazarov, S.A., Plamenevskii, B.A.: Asymptotische Theorie elliptischer Rand-wertaufgaben in singul??r gest??rten Gebieten, vol.??1, p. 432. Akademie Verlag, Berlin (1991);","key":"#cr-split#-14_CR4.1"},{"unstructured":"English transl.: Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains, vol.??1, p. 435. Birkh??user Verlag, Basel (2000)","key":"#cr-split#-14_CR4.2"},{"doi-asserted-by":"crossref","unstructured":"Nazarov, S.A., Plamenevsky, B.A.: Elliptic Problems in Domains with Piecewise Smooth Boundaries. De Gruyter Exposition in Mathematics\u00a013 (1994), Walter de Gruyter","key":"14_CR5","DOI":"10.1515\/9783110848915"},{"issue":"3-4","key":"14_CR6","doi-asserted-by":"crossref","first-page":"159","DOI":"10.3233\/ASY-2008-862","volume":"56","author":"S.A. Nazarov","year":"2008","unstructured":"Nazarov, S.A., Soko\u0142owski, J.: Spectral problems in the shape optimisation. Singular boundary perturbations. Asymptotic Analysis\u00a056(3-4), 159\u2013204 (2008)","journal-title":"Asymptotic Analysis"},{"key":"14_CR7","first-page":"867","volume":"5","author":"J.R. Roche","year":"1996","unstructured":"Roche, J.R., Soko\u0142owski, J.: Numerical methods for shape identification problems. Special issue of Control and Cybernetics: Shape Optimization and Scientific Computations\u00a05, 867\u2013894 (1996)","journal-title":"Special issue of Control and Cybernetics: Shape Optimization and Scientific Computations"},{"unstructured":"Shumacher, A.: Topologieoptimierung von Bauteilstrukturen unter Verwendung von Lochpositionierungskriterien. Ph.D. Thesis, Universit\u00e4t-Gesamthochschule-Siegen, Siegen (1995)","key":"14_CR8"},{"key":"14_CR9","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-58106-9","volume-title":"Introduction to Shape Optimization. Shape Sensitivity Analysis","author":"J. Soko\u0142owski","year":"1992","unstructured":"Soko\u0142owski, J., Zolesio, J.-P.: Introduction to Shape Optimization. Shape Sensitivity Analysis. Springer, Berlin (1992)"},{"issue":"1","key":"14_CR10","doi-asserted-by":"publisher","first-page":"145","DOI":"10.1007\/s00211-005-0635-0","volume":"102","author":"J. Soko\u0142owski","year":"2005","unstructured":"Soko\u0142owski, J., \u017bochowski, A.: Modeling of topological derivatives for contact problems. Numerische Mathematik\u00a0102(1), 145\u2013179 (2005)","journal-title":"Numerische Mathematik"},{"issue":"4","key":"14_CR11","doi-asserted-by":"publisher","first-page":"1251","DOI":"10.1137\/S0363012997323230","volume":"37","author":"J. Soko\u0142owski","year":"1999","unstructured":"Soko\u0142owski, J., \u017bochowski, A.: On topological derivative in shape optimization. SIAM Journal on Control and Optimization\u00a037(4), 1251\u20131272 (1999)","journal-title":"SIAM Journal on Control and Optimization"},{"key":"14_CR12","doi-asserted-by":"publisher","first-page":"535","DOI":"10.1016\/0893-6080(90)90004-5","volume":"3","author":"H. White","year":"1990","unstructured":"White, H.: Connectionist Nonparametric Regression: Multilayer Feedforward Networks Can Learn Arbitrary Mappings. Neural Networks\u00a03, 535\u2013549 (1990)","journal-title":"Neural Networks"}],"container-title":["IFIP Advances in Information and Communication Technology","System Modeling and Optimization"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-04802-9_14","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,2,12]],"date-time":"2025-02-12T23:11:52Z","timestamp":1739401912000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-04802-9_14"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009]]},"ISBN":["9783642048012","9783642048029"],"references-count":13,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-04802-9_14","relation":{},"ISSN":["1868-4238","1868-422X"],"issn-type":[{"type":"print","value":"1868-4238"},{"type":"electronic","value":"1868-422X"}],"subject":[],"published":{"date-parts":[[2009]]}}}