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Neural network augmented inverse problems for PDEs
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
2017 (English)In: Article in journal (Refereed) Submitted
Abstract [en]

In this paper we show how to augment classical methods for inverse problems with artificial neural networks. The neural network acts as a parametric container for the coefficient to be estimated from noisy data. Neural networks are global, smooth function approximators and as such they do not require regularization of the error functional to recover smooth solutions and coefficients. We give detailed examples using the Poisson equation in 1, 2, and 3 space dimensions and show that the neural network augmentation is robust with respect to noisy data, mesh, and geometry.

Place, publisher, year, edition, pages
2017.
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-337415OAI: oai:DiVA.org:uu-337415DiVA, id: diva2:1169415
Available from: 2017-12-27 Created: 2017-12-27 Last updated: 2017-12-27

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CiteExportLink to record
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