Machine-Learning-Based Mapping of the Ising Model to Rough Surfaces

Korsak, Sevastianos

dc.contributor.author	Korsak, Sevastianos	en
dc.date.accessioned	2022-02-28T09:25:06Z
dc.date.available	2022-02-28T09:25:06Z
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/54863
dc.identifier.uri	http://dx.doi.org/10.26240/heal.ntua.22561
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	Ising model	en
dc.subject	Mapping	en
dc.subject	Machine Learning	en
dc.subject	Magnetism	en
dc.subject	Ferromagnetism	en
dc.subject	Complexity	en
dc.subject	Complexity Measures	en
dc.title	Machine-Learning-Based Mapping of the Ising Model to Rough Surfaces	en
dc.contributor.department	Εθνικό Μετσόβιο Πολυτεχνείο--Μεταπτυχιακή Εργασία. Διεπιστημονικό-Διατμηματικό Πρόγραμμα Μεταπτυχιακών Σπουδών (Δ.Π.Μ.Σ.) “Μαθηματική Προτυποποίηση σε Σύγχρονες Τεχνολογίες και στα Χρηματοοικονομικά”	el
heal.type	masterThesis
heal.classification	Complex Systems	en
heal.classification	Computational Physics	en
heal.classification	Pattern Recognition	en
heal.classification	Theoretical Physics	en
heal.classification	Discrete Systems	en
heal.language	en
heal.access	free
heal.recordProvider	ntua	el
heal.publicationDate	2021-07-22
heal.abstract	In this master’s thesis we created a mapping between Ising model and Gaussian Rough Surfaces. To reach our goal, we studied the complexity measures of the article ‘How Complex Is Your Classification Problem?: A Survey on Measuring Classification Complexity’ by Ana C. Lorena, Luis P. F. Garcia, Jens Lehnmann, Marcilio C. P. Souto, Tim Kam Ho, and so on we defined some new complexity measures inspired from Boltzmann Machines algorithm. Some of these complexity measures give us information for the critical region of Ising model and thus can be used as diagnostics for a new simulation algorithm. In this manner, using the Rough Surfaces simulation algorithm, which was proposed by Yang, Li, Wang, and Hong in their article with title ‘Numerical Simulation of 3D Rough Surfaces and Analysis of Interfacial Contact Characteristics’, comparing these results with Metropolis-Hastings algorithm in respect to two similarity measures and using some Machine Learning techniques, we succeeded to create an algorithm that give very similar results to Ising model’s. To reassure the good behavior of the algorithm, we computed some known statistical quantities (i.e. mean magnetization, susceptibility or correlation functions), and some complexity measures that we defined in previous chapters of the thesis. Finally, we ended up in the conclusion that we can create a new simulation algorithm using Gaussian Rough Surfaces, which has the advantage that can produce lattices in equilibrium, avoiding burn-in period, with very low autocorrelations in respect to time. Moreover, our approach can be seen as a connection between a dynamical model like this of Ising, and a geometrically-based algorithm like Rough Surfaces simulation.	en
heal.advisorName	Diakonos, Fotis
heal.advisorName	Costantoudis, Vasilios
heal.committeeMemberName	Provata, Astero
heal.committeeMemberName	Costantoudis, Vasilios	en
heal.committeeMemberName	Diakonos, Fotis
heal.academicPublisher	Εθνικό Μετσόβιο Πολυτεχνείο. Σχολή Εφαρμοσμένων Μαθηματικών και Φυσικών Επιστημών	el
heal.academicPublisherID	ntua
heal.numberOfPages	124 σ.	el
heal.fullTextAvailability	false