Universität zu Köln

Grimm, Viktor Hermann ORCID: 0000-0001-5300-3705 (2023). Physics-Aware Convolutional Neural Networks for Computational Fluid Dynamics. PhD thesis, Universität zu Köln.

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Abstract

Determining the behavior of fluids is of interest in many fields. In this work, we focus on incompressible, viscous, Newtonian fluids, which are well described by the incompressible Navier-Stokes equations. A common approach to solve them approximately is to perform Computational Fluid Dynamics (CFD) simulations. However, CFD simulations are very expensive and must be repeated if the geometry changes even slightly. We consider Convolutional Neural Networks (CNNs) as surrogate models for CFD simulations for various geometries. This can also be considered as operator learning. Typically, these models are trained on images of high-fidelity simulation results. The generation of this high-fidelity training data is expensive, and a fully data-driven approach usually requires a large data set. Therefore, we are interested in training a CNN in the absence of abundant training data. To this end, we leverage the underlying physics in the form of the governing equations to construct physical constraints that we then use to train a CNN. We present results for various model problems, including two- and three-dimensional flow in channels around obstacles of various sizes and in non-rectangular geometries, especially arteries and aneurysms. We compare our novel physics-aware approach to the state-of-the-art data-based approach and also to a combination of the two, a combined or hybrid approach. In addition, we present results for an extension of our approach to include variations in the boundary conditions.

Item Type:	Thesis (PhD thesis)
Creators:	Creators Email ORCID ORCID Put Code Grimm, Viktor Hermann viktor.grimm@uni-koeln.de orcid.org/0000-0001-5300-3705 UNSPECIFIED
URN:	urn:nbn:de:hbz:38-707066
Date:	11 August 2023
Language:	English
Faculty:	Faculty of Mathematics and Natural Sciences
Divisions:	Faculty of Mathematics and Natural Sciences > Department of Mathematics and Computer Science > Mathematical Institute
Subjects:	Natural sciences and mathematics Mathematics
Uncontrolled Keywords:	Keywords Language Computational Fluid Dynamics, Machine Learning, Neural Networks, Scientific Machine Learning, physics-informed Machine Learning, surrogate model, operator learning English
Date of oral exam:	10 July 2023
Referee:	Name Academic Title Klawonn, Axel Prof. Dr. Oliver, Rheinbach Prof. Dr. Stefan, Wesner Prof. Dr.
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/70706