@PhDThesis{Sautter:2023:EnApIn,
author = "Sautter, Rubens Andreas",
title = "Gradient pattern analysis: enhancements and applications including
the influence of noise on pattern formation",
school = "Instituto Nacional de Pesquisas Espaciais (INPE)",
year = "2023",
address = "S{\~a}o Jos{\'e} dos Campos",
month = "2023-08-11",
keywords = "gradient pattern analysis, spatiotemporal pattern formation,
nonlinear fluctuations, stochastic complex Ginzburg-Landau,
structures in space physics, an{\'a}lise de padr{\~o}es
gradiente, forma{\c{c}}{\~a}o de padr{\~o}es
espa{\c{c}}o-temporais, flutua{\c{c}}{\~o}es n{\~a}o-lineares,
equa{\c{c}}{\~a}o complexa estoc{\'a}stica de Ginzburg-Landau,
estruturas em f{\'{\i}}sica espacial.",
abstract = "This doctoral project in applied computing enhances and evaluates
the performance of the Gradient Pattern Analysis (GPA) technique
in characterizing the spatiotemporal pattern formation processes
generated from the multidimensional Stochastic Complex
Ginzburg-Landau (SCGL) model. It is verified that the inclusion of
noise, forming a stochastic extended system, leads to vortices and
spiral defects that are structures resulting from the breaking of
localized gradient symmetries which is compatible with the main
GPA measurement criteria. The influence of the colored noise model
(additive and multiplicative) on the formation of such patterns is
investigated with an improved version of the GPA. For this, we
present a refinement of the GPA considering two new increments:
(i) A more precise metric to measure the phase fluctuation of the
gradient lattice corresponding to each {{snapshot;}} and (ii) a
new Lyapunov stability analysis of the reactive part is considered
to evaluate which of the colored noises results in the highest
rate of asymmetric fluctuations. Considering the stochastic model
studied in this work, the stability analysis indicates that white
and pink noise do not contribute to the formation of asymmetric
fluctuations in the reactive phase space, while red noise is
effective. Furthermore, based on the GPA measurements for modulus
(G2) and phase (G3), we show that the SCGL multiplicative red
noise model presents greater structural coherence in the
generation of spiral defects than the additive model. Based on
these results, applications of incremental GPA in a future machine
learning context are presented, taking as examples data frames
related to pattern formation processes in solar physics,
cosmology, and medicine. RESUMO: Este projeto de doutorado em
computa{\c{c}}{\~a}o aplicada aprimora e avalia o desempenho da
t{\'e}cnica Gradient Pattern Analysis (GPA) na
caracteriza{\c{c}}{\~a}o dos processos de forma{\c{c}}{\~a}o
de padr{\~o}es espa{\c{c}}o-temporais gerados a partir do modelo
multidimensional, complexo e estoc{\'a}stico, de Ginzburg-Landau
(SCGL). Verifica-se que a inclus{\~a}o de ru{\'{\i}}do,
formando um sistema estendido estoc{\'a}stico, leva a
v{\'o}rtices e defeitos espirais que s{\~a}o estruturas
coerentes resultantes da quebra de simetrias localizadas
compat{\'{\i}}veis com os principais crit{\'e}rios de medidas
do GPA. A influ{\^e}ncia do modelo de ru{\'{\i}}do colorido
(aditivo e multiplicativo) na forma{\c{c}}{\~a}o de tais
padr{\~o}es {\'e} investigada com uma vers{\~a}o melhorada do
GPA. Para isso, apresentamos um refinamento do GPA considerando
dois novos incrementos: (i) Uma m{\'e}trica mais precisa para
medir a flutua{\c{c}}{\~a}o de fase da grade gradiente
correspondente a cada {{instant{\^a}neo;}} e (ii) uma nova
an{\'a}lise de estabilidade de Lyapunov da parte reativa {\'e}
considerada para avaliar qual dos ru{\'{\i}}dos coloridos
resulta na maior taxa de flutua{\c{c}}{\~o}es assim{\'e}tricas.
Considerando o modelo estoc{\'a}stico estudado neste trabalho, a
an{\'a}lise de estabilidade indica que os ru{\'{\i}}dos branco
e rosa n{\~a}o contribuem para a forma{\c{c}}{\~a}o de
flutua{\c{c}}{\~o}es assim{\'e}tricas no espa{\c{c}}o de fase
reativa, enquanto o ru{\'{\i}}do vermelho {\'e} efetivo.
Al{\'e}m disso, com base nas medidas de GPA para m{\'o}dulo (G2)
e fase (G3), mostramos que o modelo SCGL com ru{\'{\i}}do
vermelho multiplicativo apresenta maior coer{\^e}ncia estrutural
na gera{\c{c}}{\~a}o de defeitos espirais do que o modelo
aditivo. Com base nesses resultados, s{\~a}o apresentadas
aplica{\c{c}}{\~o}es de GPA incremental em um futuro contexto de
aprendizado de m{\'a}quina, tomando como exemplos dataframes
relacionados a processos de forma{\c{c}}{\~a}o de padr{\~o}es
em f{\'{\i}}sica solar, cosmologia e medicina.",
committee = "Stephany, Stephan (presidente) and Rosa, Reinaldo Roberto
(orientador) and Santos, Leonardo Bacelar Lima and Fenton, Flavio
Hern{\'a}ndez and Rempel, {\'E}rico Luiz",
englishtitle = "An{\'a}lise de padr{\~o}es gradiente: Aprimoramentos e
aplica{\c{c}}{\~o}es incluindo a influ{\^e}ncia do
ru{\'{\i}}do na forma{\c{c}}{\~a}o de padr{\~o}es",
language = "en",
pages = "94",
ibi = "8JMKD3MGP3W34T/49M7R4L",
url = "http://urlib.net/ibi/8JMKD3MGP3W34T/49M7R4L",
targetfile = "publicacao.pdf",
urlaccessdate = "15 jun. 2024"
}