Evolution of differential models for concrete complex systems through genetic programming

Created by W.Langdon from gp-bibliography.bib Revision:1.8208

@PhdThesis{phd/hal/SantosPeretta15,

• author = "Igor {Santos Peretta}",
• title = "Evolution of differential models for concrete complex systems through genetic programming",
• title_pt = "Evolucao de modelos diferenciais para sistemas complexos concretos por Programacao Genetica",
• title_fr = "Evolution de modeles differentiels de systemes complexes concrets par Programmation Genetique",
• year = "2015",
• school = "Laboratoire des sciences de l'ingenieur, de l'informatique et de l'imagerie (ICube), Universite de Strasbourg (UNISTRA)",
• school_br = "Universidade Federal de Uberlandia",
• address = "France",
• month = sep # "~21",
• keywords = "genetic algorithms, genetic programming, GPU, CUDA, EASEA, computer-automated system modelling, differential models, linear ordinary differential equations, linear partial differential equations, fitness evaluation, Mod{\'e}lisation des syst{\`e}mes automatis{\'e}e par l'ordinateur, Mod{\`e}les diff{\'e}rentiels, {\'E}quations diff{\'e}rentielles ordinaires lin{\'e}aires, {\'E}quations diff{\'e}rentielles partielles lin{\'e}aires, Score d'adaptation, Programmation g{\'e}n{\'e}tique",
• number = "2015STRAD031",
• hal_id = "tel-01332289",
• hal_version = "v1",
• identifier = "NNT",
• language = "en",
• oai = "oai:HAL:tel-01332289v1",
• bibdate = "2016-08-08",
• bibsource = "OAI-PMH server at api.archives-ouvertes.fr",
• bibsource = "DBLP, http://dblp.uni-trier.de/https://tel.archives-ouvertes.fr/tel-01332289",
• type = "info:eu-repo/semantics/doctoralThesis; Theses",
• URL = "https://tel.archives-ouvertes.fr/tel-01332289",
• URL = "https://tel.archives-ouvertes.fr/tel-01332289/document",
• URL = "https://tel.archives-ouvertes.fr/tel-01332289/file/Santos-Peretta_Igor_2015_ED269.pdf",
• size = "127 pages",
• abstract = "A system is defined by its entities and their interrelations in an environment which is determined by an arbitrary boundary. Complex systems exhibit emergent behaviour without a central controller. Concrete systems designate the ones observable in reality. A model allows us to understand, to control and to predict behaviour of the system. A differential model from a system could be understood as some sort of underlying physical law depicted by either one or a set of differential equations. This work aims to investigate and implement methods to perform computer-automated system modelling. This thesis could be divided into three main stages: (1) developments of a computer-automated numerical solver for linear differential equations, partial or ordinary, based on the matrix formulation for an own customization of the Ritz-Galerkin method; (2) proposition of a fitness evaluation scheme which benefits from the developed numerical solver to guide evolution of differential models for concrete complex systems; (3) preliminary implementations of a genetic programming application to perform computer-automated system modelling. In the first stage, it is shown how the proposed solver uses Jacobi orthogonal polynomials as a complete basis for the Galerkin method and how the solver deals with auxiliary conditions of several types. Polynomial approximate solutions are achieved for several types of linear partial differential equations, including hyperbolic, parabolic and elliptic problems. In the second stage, the proposed fitness evaluation scheme is developed to exploit some characteristics from the proposed solver and to perform piecewise polynomial approximations in order to evaluate differential individuals from a given evolutionary algorithm population. Finally, a preliminary implementation of a genetic programming application is presented and some issues are discussed to enable a better understanding of computer-automated system modelling. Indications for some promising subjects for future continuation researches are also addressed here, as how to expand this work to some classes of non-linear partial differential equations.",
• abstract = "Un syst{\`e}me est d{\'e}fini par les entit{\'e}s et leurs interrelations dans un environnement qui est d{\'e}termin{\'e} par une limite arbitraire. Les syst{\`e}mes complexes pr{\'e}sentent un comportement {\'e}mergent sans un contr{\^o}leur central. Les syst{\`e}mes concrets d{\'e}signent ceux qui sont observables dans la r{\'e}alit{\'e}. Un mod{\`e}le nous permet de comprendre, de contr{\^o}ler et de pr{\'e}dire le comportement du syst{\`e}me. Un mod{\`e}le diff{\'e}rentiel {\`a} partir d'un syst{\`e}me pourrait {\^e}tre compris comme une sorte de loi physique sous-jacent repr{\'e}sent{\'e} par l'un ou d'un ensemble d'{\'e}quations diff{\'e}rentielles. Ce travail vise {\`a} {\'e}tudier et mettre en {\oe}uvre des m{\'e}thodes pour effectuer la mod{\'e}lisation des syst{\`e}mes automatis{\'e}e par l'ordinateur. Cette th{\`e}se pourrait {\^e}tre divis{\'e}e en trois {\'e}tapes principales, ainsi: (1) le d{\'e}veloppement d'un solveur num{\'e}rique automatis{\'e} par l'ordinateur pour les {\'e}quations diff{\'e}rentielles lin{\'e}aires, partielles ou ordinaires, sur la base de la formulation de matrice pour une personnalisation propre de la m{\'e}thode Ritz-Galerkin; (2) la proposition d'un sch{\`e}me de score d'adaptation qui b{\'e}n{\'e}ficie du solveur num{\'e}rique d{\'e}velopp{\'e} pour guider l'{\'e}volution des mod{\`e}les diff{\'e}rentiels pour les syst{\`e}mes complexes concrets; (3) une impl{\'e}mentation pr{\'e}liminaire d'une application de programmation g{\'e}n{\'e}tique pour effectuer la mod{\'e}lisation des syst{\`e}mes automatis{\'e}e par l'ordinateur. Dans la premi{\`e}re {\'e}tape, il est montr{\'e} comment le solveur propos{\'e} utilise les polyn{\^o}mes de Jacobi orthogonaux comme base compl{\`e}te pour la m{\'e}thode de Galerkin et comment le solveur traite des conditions auxiliaires de plusieurs types. Solutions {\`a} approximations polynomiales sont ensuite r{\'e}alis{\'e}s pour plusieurs types des {\'e}quations diff{\'e}rentielles partielles lin{\'e}aires, y compris les probl{\`e}mes hyperboliques, paraboliques et elliptiques. Dans la deuxi{\`e}me {\'e}tape, le sch{\`e}me de score d'adaptation propos{\'e} est con{\c c}u pour exploiter certaines caract{\'e}ristiques du solveur propos{\'e} et d'effectuer l'approximation polyn{\^o}miale par morceaux afin d'{\'e}valuer les individus diff{\'e}rentiels {\`a} partir d'une population fournie par l'algorithme {\'e}volutionnaire. Enfin, une mise en {\oe}uvre pr{\'e}liminaire d'une application GP est pr{\'e}sent{\'e}e et certaines questions sont discut{\'e}es afin de permettre une meilleure compr{\'e}hension de la mod{\'e}lisation des syst{\`e}mes automatis{\'e}e par l'ordinateur. Indications pour certains sujets prometteurs pour la continuation de futures recherches sont {\'e}galement abord{\'e}es dans ce travail, y compris la fa{\c c}on d'{\'e}tendre ce travail {\`a} certaines classes d'{\'e}quations diff{\'e}rentielles partielles non-lin{\'e}aires.",
• notes = "also known as \cite{santosperetta:tel-01332289}

  Supervisors: Keiji Yamanaka and Pierre Collet",

}

Genetic Programming entries for Igor Santos Peretta

Citations