prikaz prve stranice dokumenta Kolmogor-Arnold theorem based neural network with Fourier series approach
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master's thesis
Kolmogor-Arnold theorem based neural network with Fourier series approach
Split: University of Split, Faculty of Science, 2022. urn:nbn:hr:166:487925
Pavić, Stjepan
University of Split
Faculty of Science
Department of Physics

Institutional repository: Repository of Faculty of Science

Cite this document

Pavić, S. (2022). Kolmogor-Arnold theorem based neural network with Fourier series approach (Master's thesis). Split: University of Split, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:166:487925

Pavić, Stjepan. "Kolmogor-Arnold theorem based neural network with Fourier series approach." Master's thesis, University of Split, Faculty of Science, 2022. https://urn.nsk.hr/urn:nbn:hr:166:487925

Pavić, Stjepan. "Kolmogor-Arnold theorem based neural network with Fourier series approach." Master's thesis, University of Split, Faculty of Science, 2022. https://urn.nsk.hr/urn:nbn:hr:166:487925

Pavić, S. (2022). 'Kolmogor-Arnold theorem based neural network with Fourier series approach', Master's thesis, University of Split, Faculty of Science, accessed 11 July 2024, https://urn.nsk.hr/urn:nbn:hr:166:487925

Pavić S. Kolmogor-Arnold theorem based neural network with Fourier series approach [Master's thesis]. Split: University of Split, Faculty of Science; 2022 [cited 2024 July 11] Available at: https://urn.nsk.hr/urn:nbn:hr:166:487925

S. Pavić, "Kolmogor-Arnold theorem based neural network with Fourier series approach", Master's thesis, University of Split, Faculty of Science, Split, 2022. Available at: https://urn.nsk.hr/urn:nbn:hr:166:487925

Metadata
TitleKolmogor-Arnold theorem based neural network with Fourier series approach
Title (croatian)Neuralna mreža temeljena na Kolmogor-Arnoldovom teoremu s reprezentacijom funkcija Fourierovim redovima
AuthorStjepan Pavić
MentorLarisa Zoranić (mentor)
Committee memberLarisa Zoranić (predsjednik povjerenstva)
Committee memberŽeljana Bonačić Lošić (član povjerenstva)
Committee memberPetar Stipanović (član povjerenstva)
GranterUniversity of Split
Faculty of Science
(Department of Physics)
Split
Defense date and country2022-09-30, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Physics
Abstract
Current Neural Networks are based on the composition of the activation functions and a sum of linear functions. As such, they are limited in possibilities of implementing different algebras (such as Geometric Algebra), stunting the progress in the field of Physics Informed Neural Networks. This work is based on a more general Kolmogorov-Arnold (K-A) function approximation theorem and uses Fourier Series to represent the functions defined by the said theorem. The complexity of the used functions required both gradient-based and genetic algorithm optimizations in the construction of the developed algorithm. The thesis also includes the mathematical background of the K-A theorem and a general overview of neural networks. This new approach is represented in the form of said algorithm and its results. The comparison of the results for two different sinusoidal functions with those of classical neural networks shows that this new approach satisfies the given functions on the training domain and generalizes much better outside the said domain. These results are promising, and further research is needed on the proposed algorithm’s capabilities.
Abstract (croatian)
Trenutne neuronske mreže temelje se na kompoziciji aktivacijskih funkcija i zbroju linearnih funkcija. Kao takvi, ograničeni su u mogućnostima implementacije različitih algebri (kao što je geometrijska algebra), usporavajući napredak u razvoju Neuralnih Mreža koje su upoznate s Fizikom (Physics Informed Neural Networks). Ovaj se rad temelji na općenitijem teoremu o aproksimaciji Kolmogorov-Arnoldove (K-A) funkcije i koristi Fourierove redove za predstavljanje funkcija definiranih navedenim teoremom. Obzirom na kompleksnost funkcija razvijeni algoritam je spoj optimizacije pomoću gradijenta funkcije i genetskog algoritma. Diplomski rad također uključuje matematičku pozadinu K-A teorema i opći pregled neuronskih mreža. Ovaj novi pristup predstavljen je u obliku navedenog algoritma i njegovih rezultata. Usporedba rezultata za dvije različite sinusne funkcije s rezultatima klasičnih neuronskih mreža pokazuje da novi pristup zadovoljava zadane funkcije na domeni učenja i puno bolje generalizira izvan navedene domene. Pokazani rezultati su obećavajući i ukazuju na potrebu daljnjih istraživanja o mogućnostima predloženog algoritma.
Keywords
Keywords (croatian)
Languageenglish
URN:NBNurn:nbn:hr:166:487925
Study programmeTitle: Physics; specializations in: major in teaching, major in Astrophysics, major in Biophysics, major in Enviromental physics, major in Computational physics, major in Astrophysics and physics of elemental particles
Course: major in Biophysics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra fizike (magistar/magistra fizike)
Type of resourceText
File originBorn digital
Access conditionsAccess restricted to authenticated users
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Created on2023-02-20 12:51:20