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Solving Stokes Flow with Hybrid ML-Simulation Methods

Griese, Franziska and Knechtges, Philipp and Rüttgers, Alexander (2023) Solving Stokes Flow with Hybrid ML-Simulation Methods. CFC 2023, Cannes, Frankreich.

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Technical systems are becoming more and more complicated, making simulations of those even more complex and expensive. To reduce complexity and to make evaluation faster, nowadays neural networks are often used to build reduced order models that substitute these simulations. The neural networks are typically trained with data from simulations or measurements. But with this data-driven approach some natural laws like the conservation of energy, mass and momentum are not, or only poorly considered. In this talk two different hybrid approaches which both combine physical knowledge with neural networks are examined. First, we consider physics-informed neural networks which embed the differential equations into the loss function of a neural network. Second, we present our novel hybrid approach which incorporates the residual of the finite element formulation on a discretization into the loss function of a neural network. Both methods are trained without data from simulations or measurements, but rely on the partial differential equation itself. Finally, the methods are applied to a Stokes flow and evaluated with regard to the consideration of the incompressibility condition and computational complexity.

Item URL in elib:https://elib.dlr.de/196643/
Document Type:Conference or Workshop Item (Speech)
Title:Solving Stokes Flow with Hybrid ML-Simulation Methods
AuthorsInstitution or Email of AuthorsAuthor's ORCID iDORCID Put Code
Griese, FranziskaUNSPECIFIEDhttps://orcid.org/0000-0003-4116-2316141023969
Knechtges, PhilippUNSPECIFIEDhttps://orcid.org/0000-0002-4849-0593141023971
Rüttgers, AlexanderUNSPECIFIEDhttps://orcid.org/0000-0001-6347-9272UNSPECIFIED
Date:April 2023
Refereed publication:No
Open Access:No
Gold Open Access:No
In ISI Web of Science:No
Keywords:Physics Informed, FEM-based Neural Network, Machine Learning, Predictive Modeling
Event Title:CFC 2023
Event Location:Cannes, Frankreich
Event Type:international Conference
HGF - Research field:other
HGF - Program:other
HGF - Program Themes:other
DLR - Research area:Digitalisation
DLR - Program:D KIZ - Artificial Intelligence
DLR - Research theme (Project):D - PISA
Location: Köln-Porz
Institutes and Institutions:Institute for Software Technology
Deposited By: Griese, Franziska
Deposited On:23 Aug 2023 12:59
Last Modified:23 Aug 2023 12:59

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