Numerical Solution of PDE’s Using Deep Learning

Resumo

This work presents a method for the solution of partial diferential equations (PDE’s) using neural networks, more specifically deep learning. The main idea behind the method is using a function of the PDE itself as the loss function, together with the boundary conditions, based mainly on [Sirignano and Spiliopoulos, 2017]. The method uses a architecture similar to one of LSTM (Long short-term memory) recurrent neural networks, and a loss function computed on a random sample of the domain. The examples considered in this thesis come from financial mathematics, mean-field games and some other classical PDE’s.

Ficha do documento

Tipo

Dissertação

Ano

2019

Instituição

Fundação Getulio Vargas

Fonte

Repositório da FGV

Idioma

Inglês

Acesso

Não informado

Identificador

oai:repositorio.fgv.br:10438/28572

Palavras-chave

PDENeural networksMatemáticaEquações diferenciais parciaisRedes neurais (Computação)Aprendizado do computador