Advanced machine learning methods for
large-scale parametrized problems in
computational mechanics

Νικολόπουλος, Στέφανος; Nikolopoulos, Stefanos

dc.contributor.author	Νικολόπουλος, Στέφανος	el
dc.contributor.author	Nikolopoulos, Stefanos
dc.date.accessioned	2023-04-28T11:01:55Z
dc.date.available	2023-04-28T11:01:55Z
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/57598
dc.identifier.uri	http://dx.doi.org/10.26240/heal.ntua.25295
dc.rights	Αναφορά Δημιουργού-Μη Εμπορική Χρήση-Όχι Παράγωγα Έργα 3.0 Ελλάδα	*
dc.rights.uri	http://creativecommons.org/licenses/by-nc-nd/3.0/gr/	*
dc.subject	Machine Learning	en
dc.subject	Artificial Intelligence	en
dc.subject	Computational Mechanics	en
dc.subject	Surrogate Modeling	en
dc.subject	Convolutional Autoencoders	en
dc.title	Advanced machine learning methods for large-scale parametrized problems in computational mechanics	en
dc.title	Προχωρημένες μέθοδοι μηχανικής μάθησης για παραμετροποιήσιμα προβλήματα μεγάλης κλίμακας στην υπολογιστική μηχανική	el
heal.type	doctoralThesis
heal.classification	Machine Learning	en
heal.classification	Artificial Intelligence	en
heal.classification	Computational Mechanics	en
heal.language	en
heal.access	free
heal.recordProvider	ntua	el
heal.publicationDate	2023-01-01
heal.abstract	Recent advances in the field of machine learning open a new era in high performance computing for challenging computational science and engineering applications. In this framework, the use of advanced machine learning algorithms for the development of accurate and cost-efficient surrogate models of complex physical processes has already attracted major attention from scientists. This dissertation presents a novel nonintrusive surrogate modeling scheme based on deep learning for predictive modeling of complex systems, described by parametrized time-dependent partial differential equations. Specifically, the proposed method utilizes a convolutional autoencoder in conjunction with a feed forward neural network to establish a mapping from the problem’s parametric space to its solution space. For this purpose, training data are collected by solving the high-fidelity model via finite elements for a reduced set of parameter values. Then, by applying the convolutional autoencoder, a low-dimensional vector representation of the high dimensional solution matrices is provided by the encoder, while the reconstruction map is obtained by the decoder. Using the latent vectors given by the encoder, a feed forward neural network is efficiently trained to map points from the parametric space to the compressed version of the respective solution matrices. This way, the proposed surrogate model is capable of predicting the entire time history response simultaneously with remarkable computational gains and very high accuracy. The elaborated methodology is demonstrated on the stochastic analysis of time-dependent partial differential equations solved with the Monte Carlo method. However, despite their powerful approximation capabilities, surrogate model predictions are still far from being near to the ‘exact’ solution of the problem. To address this issue, this thesis suggests the use of up-to-date machine learning tools in order to equip a new generation of iterative solvers of linear equation systems, capable of very efficiently solving large-scale parametrized problems at any desired level of accuracy. The proposed approach consists of the following two steps. At first, a reduced set of model evaluations is performed using a standard finite element methodology and the corresponding solutions are used to establish an approximate mapping from the problem’s parametric space to its solution space using a combination of deep feedforward neural networks and convolutional autoencoders. This mapping serves a means to obtain very accurate initial predictions of the system’s response to new query points at negligible computational cost. Subsequently, an iterative solver inspired by the Algebraic Multigrid method in combination with Proper Orthogonal Decomposition, termed POD-2G, is developed that successively refines the initial predictions of the surrogate model towards the exact solution. The application of POD-2G as a standalone solver or as preconditioner in the context of preconditioned conjugate gradient methods is demonstrated on several numerical examples of large scale systems, with the results indicating its strong superiority over conventional iterative solution schemes. Furthermore, the development of Physics-Informed Neural Networks (PINNs) over the recent years has offered a promising avenue for the solution of partial differential equations, as well as for the identification of unknown equation parameters. The last chapter of this dissertation focuses on the application of PINNs, and in particular, their variation called eXtended PINNs (XPINNs) for the determination of the Kapitza thermal resistance at the interface between the different phases in a multiphase composite material. This phenomenological model parameter is almost impossible to measure experimentally, however the proposed framework successfully overcomes this difficulty since it only requires measurements of the temperature at the interior of the composite that are easy to obtain. The task of fine tuning the XPINN related hyperparameters is successfully addressed by employing a Bayesian hyperparameter optimisation scheme based on Gaussian process regression. Benchmark numerical examples are provided that demonstrate the high accuracy, ease of implementation and robustness of the proposed computational framework in capturing the true values of the Kapitza resistance.	en
heal.advisorName	Παπαδόπουλος, Βησσαρίων	el
heal.committeeMemberName	Παπαδόπουλος, Βησσαρίων	el
heal.committeeMemberName	Βαμβάτσικος, Δημήτριος	el
heal.committeeMemberName	Φραγκιαδάκης, Μιχαήλ	el
heal.committeeMemberName	Ζέρης, Χρήστος	el
heal.committeeMemberName	Λαγαρός, Νικόλαος	el
heal.committeeMemberName	Γεωργούλης, Εμμανουήλ	el
heal.committeeMemberName	Τριανταφύλλου, Σάββας	el
heal.academicPublisher	Εθνικό Μετσόβιο Πολυτεχνείο. Σχολή Πολιτικών Μηχανικών	el
heal.academicPublisherID	ntua
heal.fullTextAvailability	false