Study of a wind-wave numerical model and its integration with ocean and oil-spill numerical models

The ability to represent the transport and fate of an oil slick at the sea surface is a formidable task. By using an accurate numerical representation of oil evolution and movement in seawater, the possibility to asses and reduce the oil-spill pollution risk can be greatly improved. The blowing of the wind on the sea surface generates ocean waves, which give rise to transport of pollutants by wave-induced velocities that are known as Stokes’ Drift velocities. The Stokes’ Drift transport associated to a random gravity wave field is a function of the wave Energy Spectra that statistically fully describe it and that can be provided by a wave numerical model. Therefore, in order to perform an accurate numerical simulation of the oil motion in seawater, a coupling of the oil-spill model with a wave forecasting model is needed. In this Thesis work, the coupling of the MEDSLIK-II oil-spill numerical model with the SWAN wind-wave numerical model has been performed and tested. In order to improve the knowledge of the wind-wave model and its numerical performances, a preliminary sensitivity study to different SWAN model configuration has been carried out. The SWAN model results have been compared with the ISPRA directional buoys located at Venezia, Ancona and Monopoli and the best model settings have been detected. Then, high resolution currents provided by a relocatable model (SURF) have been used to force both the wave and the oil-spill models and its coupling with the SWAN model has been tested. The trajectories of four drifters have been simulated by using JONSWAP parametric spectra or SWAN directional-frequency energy output spectra and results have been compared with the real paths traveled by the drifters.

Quantum solitons in the XXZ model with staggered external magnetic field

The 1-D 1/2-spin XXZ model with staggered external magnetic field, when restricting to low field, can be mapped into the quantum sine-Gordon model through bosonization: this assures the presence of soliton, antisoliton and breather excitations in it. In particular, the action of the staggered field opens a gap so that these physical objects are stable against energetic fluctuations. In the present work, this model is studied both analytically and numerically. On the one hand, analytical calculations are made to solve exactly the model through Bethe ansatz: the solution for the XX + h staggered model is found first by means of Jordan-Wigner transformation and then through Bethe ansatz; after this stage, efforts are made to extend the latter approach to the XXZ + h staggered model (without finding its exact solution). On the other hand, the energies of the elementary soliton excitations are pinpointed through static DMRG (Density Matrix Renormalization Group) for different values of the parameters in the hamiltonian. Breathers are found to be in the antiferromagnetic region only, while solitons and antisolitons are present both in the ferromagnetic and antiferromagnetic region. Their single-site z-magnetization expectation values are also computed to see how they appear in real space, and time-dependent DMRG is employed to realize quenches on the hamiltonian parameters to monitor their time-evolution. The results obtained reveal the quantum nature of these objects and provide some information about their features. Further studies and a better understanding of their properties could bring to the realization of a two-level state through a soliton-antisoliton pair, in order to implement a qubit.

Limiting theorems in statistical mechanics. The mean-field case.

The Curie-Weiss model is defined by ah Hamiltonian according to spins interact. For some particular values of the parameters, the sum of the spins normalized with square-root normalization converges or not toward Gaussian distribution. In the thesis we investigate some correlations between the behaviour of the sum and the central limit for interacting random variables.

Meta-learning for informed model searches in Automated Machine Learning

Day by day, machine learning is changing our lives in ways we could not have imagined just 5 years ago. ML expertise is more and more requested and needed, though just a limited number of ML engineers are available on the job market, and their knowledge is always limited by an inherent characteristic of theirs: they are humans. This thesis explores the possibilities offered by meta-learning, a new field in ML that takes learning a level higher: models are trained on other models' training data, starting from features of the dataset they were trained on, inference times, obtained performances, to try to understand the relationship between a good model and the way it was obtained. The so-called metamodel was trained on data collected by OpenML, the largest ML metadata platform that's publicly available today. Datasets were analyzed to obtain meta-features that describe them, which were then tied to model performances in a regression task. The obtained metamodel predicts the expected performances of a given model type (e.g., a random forest) on a given ML task (e.g., classification on the UCI census dataset). This research was then integrated into a custom-made AutoML framework, to show how meta-learning is not an end in itself, but it can be used to further progress our ML research. Encoding ML engineering expertise in a model allows better, faster, and more impactful ML applications across the whole world, while reducing the cost that is inevitably tied to human engineers.

Machine Learning in Automatic Tabulation for Constraint Model Reformulation

Combinatorial decision and optimization problems belong to numerous applications, such as logistics and scheduling, and can be solved with various approaches. Boolean Satisfiability and Constraint Programming solvers are some of the most used ones and their performance is significantly influenced by the model chosen to represent a given problem. This has led to the study of model reformulation methods, one of which is tabulation, that consists in rewriting the expression of a constraint in terms of a table constraint. To apply it, one should identify which constraints can help and which can hinder the solving process. So far this has been performed by hand, for example in MiniZinc, or automatically with manually designed heuristics, in Savile Row. Though, it has been shown that the performances of these heuristics differ across problems and solvers, in some cases helping and in others hindering the solving procedure. However, recent works in the field of combinatorial optimization have shown that Machine Learning (ML) can be increasingly useful in the model reformulation steps. This thesis aims to design a ML approach to identify the instances for which Savile Row’s heuristics should be activated. Additionally, it is possible that the heuristics miss some good tabulation opportunities, so we perform an exploratory analysis for the creation of a ML classifier able to predict whether or not a constraint should be tabulated. The results reached towards the first goal show that a random forest classifier leads to an increase in the performances of 4 different solvers. The experimental results in the second task show that a ML approach could improve the performance of a solver for some problem classes.