Applications of Topological Derivatives and Neural Networks for Inverse Problems

DOI10.1007/978-3-642-04802-9_14zbMath1188.35203OpenAlexW18688361MaRDI QIDQ3557814

Marta Grzanek, Katarzyna Szulc

Publication date: 23 April 2010

Published in: IFIP Advances in Information and Communication Technology (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-642-04802-9_14

zbMATH Keywords

neural networksinverse problemsshape optimizationmicrocrack

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Geometric methods (93B27) Contact in solid mechanics (74M15) Inverse problems for PDEs (35R30) Circuits, networks (94C99) Optimization of shapes other than minimal surfaces (49Q10) Numerical methods for inverse problems for boundary value problems involving PDEs (65N21) Inverse problems in optimal control (49N45) Topological and monotonicity methods applied to PDEs (35A16)

Cites Work

• Elliptic problems in domains with piecewise smooth boundaries
• On numerical solution of shape inverse problems
• Modelling of topological derivatives for contact problems
• On the Topological Derivative in Shape Optimization
• Universal approximation bounds for superpositions of a sigmoidal function
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