Sobolev neural network with residual weighting as a surrogate in linear and non-linear mechanics

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dc.contributor.authorKilicsoy, Ali Osman Mert
dc.contributor.authorLiedmann, Jan
dc.contributor.authorValdebenito, Marcos A.
dc.contributor.authorBarthold, Franz-Joseph
dc.contributor.authorFaes, Matthias G. R.
dc.date.accessioned2025-07-07T10:23:34Z
dc.date.available2025-07-07T10:23:34Z
dc.date.issued2024-09-23
dc.description.abstractAreas of computational mechanics such as uncertainty quantification and optimization usually involve repeated evaluation of numerical models that represent the behavior of engineering systems. In the case of complex non-linear systems however, these models tend to be expensive to evaluate, making surrogate models quite valuable. Artificial neural networks approximate systems very well by taking advantage of the inherent information of its given training data. In this context, this paper investigates the improvement of the training process by including sensitivity information, which are partial derivatives w.r.t. inputs, as outlined by Sobolev training. In computational mechanics, sensitivities can be applied to neural networks by expanding the training loss function with additional loss terms, thereby improving training convergence resulting in lower generalisation error. This improvement is shown in two examples of linear and non-linear material behavior. More specifically, the Sobolev designed loss function is expanded with residual weights adjusting the effect of each loss on the training step. Residual weighting is the given scaling to the different training data, which in this case are response and sensitivities. These residual weights are optimized by an adaptive scheme, whereby varying objective functions are explored, with some showing improvements in accuracy and precision of the general training convergence.en
dc.identifier.urihttp://hdl.handle.net/2003/43790
dc.identifier.urihttp://dx.doi.org/10.17877/DE290R-25564
dc.language.isoen
dc.relation.ispartofseriesIEEE access; 12
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.subjectMachine learningen
dc.subjectSobolev trainingen
dc.subjectresidual weightingen
dc.subjectfinite element modellingen
dc.subjectlinear and non-linear mechanicsen
dc.subjectneural networksen
dc.subjectoptimizationen
dc.subjectsurrogate modelen
dc.subject.ddc620
dc.subject.rswkMaschinelles Lernen
dc.subject.rswkSobolev-Raum
dc.subject.rswkGewichtung
dc.subject.rswkFinite-Elemente-Methode
dc.subject.rswkStatistische Mechanik
dc.subject.rswkNeuronales Netz
dc.subject.rswkOptimierung
dc.titleSobolev neural network with residual weighting as a surrogate in linear and non-linear mechanicsen
dc.typeText
dc.type.publicationtypeResearchArticle
dcterms.accessRightsopen access
eldorado.secondarypublicationtrue
eldorado.secondarypublication.primarycitationA. O. M. Kilicsoy, J. Liedmann, M. A. Valdebenito, F.-J. Barthold, und M. G. R. Faes, „Sobolev neural network with residual weighting as a surrogate in linear and non-linear mechanics“, IEEE access, Bd. 12, S. 137144–137161, 2024, doi: 10.1109/access.2024.3465572
eldorado.secondarypublication.primaryidentifierhttps://doi.org/10.1109/ACCESS.2024.3465572

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