Ανάλυση διάδοσης κύματος με καθοδηγούμενα από τη φυσική τεχνητά νευρωνικά δίκτυα

Vlachopoulou, Adamantia; Βλαχοπούλου, Αδαμαντία

dc.contributor.author	Vlachopoulou, Adamantia	en
dc.contributor.author	Βλαχοπούλου, Αδαμαντία	el
dc.date.accessioned	2022-04-19T10:34:14Z
dc.date.available	2022-04-19T10:34:14Z
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/55114
dc.identifier.uri	http://dx.doi.org/10.26240/heal.ntua.22812
dc.rights	Default License
dc.subject	Artificial neural networks	en
dc.subject	Euler-Bernoulli equation of beams	en
dc.subject	Modal analysis	en
dc.subject	Nonlinear partial differential equations	en
dc.subject	Physics Informed Neural Networks (ΡΙΝΝs)	en
dc.title	Ανάλυση διάδοσης κύματος με καθοδηγούμενα από τη φυσική τεχνητά νευρωνικά δίκτυα	el
heal.type	bachelorThesis
heal.secondaryTitle	Wave propagation analysis using Physics Informed Neural Networks	en
heal.classification	artificial neural nerworks	el
heal.access	free
heal.recordProvider	ntua	el
heal.publicationDate	2021-11-05
heal.abstract	The solution of nonlinear partial differential equations using numerical methods is an arduous, in cases complex, and computationally taxing procedure. In this thesis, the efficiency of machine learning as a means to rapidly tackle the solution of nonlinear partial differential equations is examined. To this end, a new methodology for solving complex problems has recently emerged in the literature, i.e., Physics Informed Neural Networks (PINNs). This involves the utilization of artificial neural networks that obey a physical law and hence are described by nonlinear partial differential equations. Based on the nature of the problem and the available data, two classes of problems may be determined, i.e., those that aim at finding the solution of the equation that describes the physical problem and those that aim at estimating the parameters of the equation for a given known solution. In this thesis, the robustness and accuracy of PINNs to tackle partial differential equations is examined. As a first step, the case of the nonlinear Burgers equation is investigated. Next, the case of elastic waves propagating in beams is examined. To this end, both the inference and the identification problem were addressed for the beam wave equation using PINNs and the results were compared with the analytical solution obtained through modal analysis. It has been observed that PINNs can accurately estimate the solution of this differential equation and estimate its parameters, while within the spatial and temporal scale that neural network has been trained. It established that there was a difference between the exact and predicted values of the beam boundary conditions.	el
heal.advisorName	Savas, Triantafillou	en
heal.committeeMemberName	Papadopoulos, Visarion, Maria Nerantzaki	en
heal.academicPublisher	Εθνικό Μετσόβιο Πολυτεχνείο. Σχολή Πολιτικών Μηχανικών	el
heal.academicPublisherID	ntua
heal.fullTextAvailability	false