- Lucas Farias Lima
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.
*Texto enviado pelo aluno.
Membros da banca:
- Yuri Fahham Saporito (orientador) - FGV EMAp
- Hugo Alexander de la Cruz Cansino – FGV EMAp
- Emilio Vital Brazil (IBM)