Name: Wilson Guasti Junior
Type: MSc dissertation
Publication date: 25/03/2021
Advisor:

Name Rolesort descending
Isaac Pinheiro dos Santos Advisor *

Examining board:

Name Rolesort descending
Lucia Catabriga Advisor *
Isaac Pinheiro dos Santos Advisor *

Summary: The study of differential equations plays an important role in several fields of science and
technology, through the modeling of real-world problems. As most of the mathematical models
described by differential equations (ordinary and partial) do not have an analytical solution,
numerical methods, such as finite differences and finite elements, are widely used to solve
it. Recently, many studies have been dedicated to the application of deep artificial neural
networks, known as deep learning, in the solution of differential equations, with promising
results.
The aim of this work is to explore the use of artificial neural networks feedforward in the
solution of ordinary and partial differential equations. The neural network was implemented
using the Python language, with the Tensorflow library. We applied this methodology in
the solution of two initial value problems, in the Poisson problem (two-dimensional), in two
unsteady problems (heat and wave equations) and in a singularly perturbed one-dimensional
problem (convection-diffusion equation) to evaluate the quality of the solutions obtained
. Some comparisons with classical numerical methods, such as Euler, Runge-Kutta, finite
differences and finite elements, are presented.
Keywords: Differential Equations. Artificial Neural Networks. Tensorflow. Deep Learning.

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