Machine Learning for Nonlinear Inverse Problems

There have been multiple mathematical models presented by scientists that allow cor- roborating the behavior of complex systems. However, these models estimate values that can be measured but are unable to determine the parameters that caused such behaviors. Inverse Problems aim at finding the parameters of a model, given by systems of equa- tions, from noisy observations/measurements. These are typically ill-posed problems that may have no exact solutions, multiple solutions or unstable solutions. In this the- sis, we will be restringing our work to nonlinear inverse problems that have an exact single solution but due to their complexity can not be computed analytically and a small uncertainty in the measurements may induce a large uncertainty in the solutions. Our approach resorts to deep learning techniques in order to support reasoning for this family of non-linear inverse problems. In this thesis, we will employ the forward model to generate the dataset used to train the neural network which is going to be used as a regression model to approximate the desired inverse function. This work will be applied to a research area widely used in climate change studies with potential applications in water quality monitoring, denominated Ocean Color. We aim to obtain a model that is capable of accurately estimating the concentration of active seawater compounds, from remote sensing measurements of the sea surface reflectance taking into consideration the impact of uncertainty on the sensor observations and the model approximations.Houve múltiplos modelos matemáticos propostos por cientistas que permitem cor- roborar o comportamento de sistemas complexos. No entanto, estes modelos estimam valores que podem ser medidos porém são incapazes de determinar os parâmetros que causaram tais comportamentos. Os problemas inversos visam encontrar os parâmetros de um modelo, dados por sis- temas de equações, a partir de observações/medições ruidosas. Estes são tipicamente problemas ill-posed que podem não ter soluções exactas, ter múltiplas soluções ou solu- ções instáveis. Nesta tese, iremos restringir o nosso trabalho a problemas inversos não lineares que devido à sua complexidade não podem ser computados analiticamente e uma pequena incerteza nas medições pode induzir uma grande incerteza nas soluções. A nossa abordagem recorre a técnicas de aprendizagem profunda com o intuito de arranjar soluções para resolver esta familia de problemas inversos não lineares. Nesta tese vamos empregar o modelo direto para gerar o conjunto de dados utilizado para treinar a rede neural que vai ser utilizado como modelo de regressão para aproximar a função inversa desejada. Este trabalho será aplicado a uma área de investigação amplamente utilizada em estu- dos sobre alterações climáticas com potenciais aplicações na monitorização da qualidade da água, denominada Ocean Color. O nosso objectivo é obter um modelo capaz de estimar com precisão a concentração de compostos activos da água do mar, a partir de medições de detecção remota da reflectância da superfície marítima, tendo em consideração o impacto da incerteza nas observações do sensor e nas aproximações do modelo

Using landscape topology to compare continuous metaheuristics: a framework and case study on EDAs and ridge structure

In this paper we extend a previously proposed randomized landscape generator in combination with a comparative experimental methodology to study the behavior of continuous metaheuristic optimization algorithms. In particular, we generate twodimensional landscapes with parameterized, linear ridge structure, and perform pairwise comparisons of algorithms to gain insight into what kind of problems are easy and difficult for one algorithm instance relative to another.We apply thismethodology to investigate the specific issue of explicit dependency modeling in simple continuous estimation of distribution algorithms. Experimental results reveal specific examples of landscapes (with certain identifiable features) where dependency modeling is useful, harmful, or has little impact on mean algorithm performance. Heat maps are used to compare algorithm performance over a large number of landscape instances and algorithm trials. Finally, we perform ameta-search in the landscape parameter space to find landscapes which maximize the performance between algorithms. The results are related to some previous intuition about the behavior of these algorithms, but at the same time lead to new insights into the relationship between dependency modeling in EDAs and the structure of the problem landscape. The landscape generator and overall methodology are quite general and extendable and can be used to examine specific features of other algorithms