Sustav za simboličku regresiju implicitnih funkcija

master's thesis

• Title (english): Implicit function symbolic regression system
• Author: Josip Mrđen
• Mentor: Domagoj Jakobović (mentor)
• Committee member: Domagoj Jakobović (predsjednik povjerenstva)
• Committee member: Marko Đurasević (član povjerenstva)
• Committee member: Marko Čupić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Electrical Engineering and Computing; Zagreb
• Defense date and country: 2020-07-14, Croatia
• Scientific / art field, discipline and subdiscipline: TECHNICAL SCIENCES; Computing

Abstract

Simbolička regresija je metoda kojom se iz skupa točaka u prostoru pokušava inferirati jednadžba sustava koji ga opisuje. S obzirom da su eksplicitne formule uglavnom bile predmet istraživanja tom metodom tokom godina, ova teza se odlučila baviti simboličkom regresijom implicitnih funkcija. Implicitne funkcije su zbog svojih određenih svojstava puno ekspresivnije te su teže za inferirati te su napravljene različite heuristike za dolazak do zadovoljavajućih rješenja. Jednostavnija metoda obuhvaćala je standardnu devijaciju kandidata rješenja problema, te se minimiziranjem raspršenosti proizvoljni algoritam navodio na konačno rješenje regresije. Druga metoda iskoristila je usporedbu parcijalnih derivacija između kandidata rješenja te eksperimentalno dobivenih derivacija. U dvodimenzionalnim sustavima računanje derivacije je jednostavno dok je za višedimenzionalne sustave potrebno odrediti ravninu u lokalnoj blizini neke središnje točke za dobivanje ispravne derivacije. Za određivanje ravnina koristila se metoda najmanjih kvadrata, te je u konačnici za određeni podskup funkcija radio vrlo dobro, dok je nad drugima potrebno ipak više istraživanja i pokušaja za dobivanje ispravnijih podataka. Heuristike su upogonjene algoritmima genetskog programiranja te genskog ekspresijskog programiranja (GEP) te su za izvjesni podskup funkcija pokazale iznimno dobre rezultate.

Abstract (english)

Symbolic regression is a method by which an equation of the system describing it is inferred from a set of points in space. Since explicit formulas have been the subject of research by this method over the years, this thesis decided to deal with the symbolic regression of implicit functions. Implicit functions are much more expressive due to their certain properties and are harder to infer than explicit ones. Therefore, different heuristics have been made to arrive at satisfactory solutions. A simpler method involved minimizing the standard deviation of evaluations for candidate solutions (equations) to the problem. By lowering the scattering for all the points in the set, the arbitrary algorithm was guided to the final solution of the regression. The second method used the comparison of partial derivations between solution equations and experimentally obtained derivatives. In two-dimensional systems, the derivation calculation is simple, while for multidimensional systems it is necessary to determine the plane in the local vicinity of some central point to obtain the correct derivation. The least squares method was used to determine the planes, and in the end it worked very well for a certain subset of functions which were conic or spherical, while more research and attempts are still needed on others to obtain more accurate data. Heuristics were driven by genetic programming algorithms and gene expression programming (GEP) which have shown extremely good results for a certain subset of functions.

• Keywords: Simbolička regresija; implicitne funkcije; genetsko programiranje; gensko ekspresijsko programiranje; metoda najmanjih kvadrata
• Keywords (english): Symbolic regression; implicit functions; genetic programming; gene expression programming; least squares method
• Language: english
• URN:NBN: urn:nbn:hr:168:283142
• Study programme: Title: Computing; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra inženjer/inženjerka računarstva (magistar/magistra inženjer/inženjerka računarstva)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Closed access
• Created on: 2023-01-13 13:16:36