| 10627042 | Data Mining [MATH-05/A] [ITA] | 1st | 2nd | 6 |
Educational objectives 1. Knowledge and understanding
Students who have passed the exam will know and understand the main tools for Data Analysis: Gaussian models, linear models, principal component analysis, factor analysis, discriminant analysis, analysis of
canonical correlation, multi-dimensional scaling, causal models, Markov chains, random graphs, graph-based algorithms.
2. Applied knowledge and understanding
Students who pass the exam will be able to solve Data Mining problems, including model selection, prediction, classification, clustering, dimension reduction, feature extraction, causal inference.
3. Making judgments
Students will be able to evaluate the results produced by their programs and to produce tests and simulations.
4. Communication skills
Students will be able to present and explain the solution of some problems and excercises either at the blackboard and/or using a computer.
5. Learning skills
The acquired knowledge will construct the basis to study more specialized topics of Data Science and the numerical methods in this area.
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| 10629409 | DISCRETE MATHEMATICS [MATH-02/A] [ITA] | 1st | 2nd | 6 |
Educational objectives General objectives: to acquire the basic knowledge and techniques of the combinatorics of permutations, enumerative combinatorics, combinatorics of integer partitions, generating functions and understand its main applications.
Specific objectives:
Knowledge and understanding: at the end of the course the student will have acquired the basic notions and results related to Combinatorics of permutations (with particular regard to enumerations, representation with trees, cycles, linear orderings, random generation) and enumerative combinatorics (especially concerning its algebraic aspects, via generating functions). She will also know at least the set of the most significant problems in which these theories find applications.
Apply knowledge and understanding: the student will be able to solve algebraic-combinatorial problems requiring the use of techniques related to the theories of combinatorics of permutations, enumerative combinatorics, of posets and integer partitions, and to discuss how problems (in non-purely mathematical environments) can be modeled by means of the acquired tools.
Critical and judgmental skills: the student will have the basis to analyze how the topics of combinatorics and Algebra and Linear Algebra treated in basic courses can find applications in different fields and be an essential tool in solving concrete problems.
Communication skills: The learner will have the ability to communicate rigorously the ideas and contents shown in the course.
Learning skills: the acquired knowledge will allow the student to carry on an autonomous study in a possible interdisciplinary context (for those who have knowledge and interests in Applied Mathematics, Genetics, Computer Science, Data Science).
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| 10630822 | Mathematical methods in Statistical Mechanics [MATH-04/A, MATH-03/B] [ITA] | 1st | 2nd | 6 |
Educational objectives General targets:
acquire basic knowledge on a rigorous approach to statistical equilibrium mechanics.
Applying knowledge and understanding:
knowledge of statistical ensembles, Gibbs measures and thermodynamic functionals; understanding of phase transitions for paradigmatic lattice particle models.
Making judgements:
ability to describe mechanical and thermodynamic behavior of large systems of particles.
Communication skills:
ability to identify the main points of the theory, to be able to illustrate the most interesting elements by using appropriate examples, and to discuss the mathematic details for simple models.
Learning skills:
the acquired knowledge will allow to face advanced studies, i.e. at PhD level, related to equilibrium and non-equilibrium statistical mechanics, and to use the basic tools of statistical mechanics in other contexts.
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| Module I - Statistical methods [MATH-04/A] [ITA] | 1st | 2nd | 3 |
Educational objectives General targets:
acquire basic knowledge on a rigorous approach to statistical equilibrium mechanics.
Applying knowledge and understanding:
knowledge of statistical ensembles, Gibbs measures and thermodynamic functionals; understanding of phase transitions for paradigmatic lattice particle models.
Making judgements:
ability to describe mechanical and thermodynamic behavior of large systems of particles.
Communication skills:
ability to identify the main points of the theory, to be able to illustrate the most interesting elements by using appropriate examples, and to discuss the mathematic details for simple models.
Learning skills:
the acquired knowledge will allow to face advanced studies, i.e. at PhD level, related to equilibrium and non-equilibrium statistical mechanics, and to use the basic tools of statistical mechanics in other contexts.
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| Module II - Physical mathematics methods [MATH-03/B] [ITA] | 1st | 2nd | 3 |
Educational objectives General targets:
acquire basic knowledge on a rigorous approach to statistical equilibrium mechanics.
Applying knowledge and understanding:
knowledge of statistical ensembles, Gibbs measures and thermodynamic functionals; understanding of phase transitions for paradigmatic lattice particle models.
Making judgements:
ability to describe mechanical and thermodynamic behavior of large systems of particles.
Communication skills:
ability to identify the main points of the theory, to be able to illustrate the most interesting elements by using appropriate examples, and to discuss the mathematic details for simple models.
Learning skills:
the acquired knowledge will allow to face advanced studies, i.e. at PhD level, related to equilibrium and non-equilibrium statistical mechanics, and to use the basic tools of statistical mechanics in other contexts.
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| 10626547 | STOCHASTIC PROCESSES [MATH-03/B] [ITA] | 1st | 2nd | 6 |
Educational objectives General objectives: to acquire basic knowledge in stochastic process theory and in stochastic modeling
of real phenomena.
Specific objectives:
Knowledge and understanding: at the end of the course the student will have acquired the basic notions and results concerning stochastic processes in discrete and continuous time, on discrete structures such as graphs or on continuous spaces.
Apply knowledge and understanding: at the end of the course the student will be able to model the temporal evolution of various real phenomena through stochastic processes, to analyze the stationarity and / or temporal reversibility of stochastic processes, to calculate probabilities of absorption and expected absorption times, to simulate stochastic processes and to estimate the rate of convergence at equilibrium.
Critical and judgmental skills: the student will have the basis to study stochastic dynamic systems and acquire the ability to evaluate the goodness of a model compared to others in the modeling of real phenomena.
Communication skills: having to take an oral theory test, students will develop the communication skills necessary to expose the mathematical theory and the various models considered in the course.
Learning skills: the acquired knowledge will allow a more in-depth study of stochastic processes both on discrete and continuous spaces, helping the student to study other courses such as stochastic calculus.
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| 10626546 | THEORY OF ALGORITHMS [INFO-01/A] [ITA] | 1st | 2nd | 6 |
Educational objectives General Goals
The course deals with some fundamental issues of contemporary research in algorithms in the field of computational complexity, probabilistic algorithms and machine learning.
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| 10626887 | Computational Mathematics [MATH-05/A] [ENG] | 1st | 2nd | 6 |
Educational objectives The course is devoted to the study of multiscale approaches (micro-meso-macro) for multi-agent systems. Typical examples are: vehicular traffic, crowd dynamics, opinion dynamics, flocking/swarming, financial markets and so on.
The course includes lab sessions for the computational part related to the numerica simulation of the models.
1. Knowledge and understanding
Students who have passed the exam will know how to model and study qualitative properties of physical phenomena through several scales of representation: from the microscopic, to the kinetic and the macroscopic one.
2. Applied knowledge and understanding
Students who have passed the exam will be able to use a efficient numerical techniques, deterministic and not, for the simulation of models, and they will be able to code the algorithms in C++ or MATLAB.
3. Making judgments
Students will be able to evaluate the right representation scale of the given phenomenon, the results produced by their programs and to produce tests and simulations.
4. Communication skills
Students will be able to present and explain the modeling choices, the properties of the models, either at the blackboard and/or using a computer.
5. Learning skills
The acquired knowledge will construct the basis to study more research topics related to the modeling of multi-agent systems.
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| 10627464 | Quantum Machine Learning [MATH-04/A] [ITA] | 1st | 2nd | 6 |
Educational objectives The main purpose of the course is to present a compact but effective introduction to the basics of quantum machine learning (QML) starting from fundamental notions of quantum mechanics and quantum computing. The idea is to explain how the foundations of quantum mechanics enable new and efficient learning schemes to students with no background in quantum mechanics and quantum computing.
Students will not merely learn how to translate classical machine learning techniques into the language of quantum computing, but rather a new approach to data representation and processing that is intrinsically different from that performed by standard computers.
The course includes lectures and classroom exercises, useful to check students' personal preparation.
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| 10631691 | ADVANCED MACHINE LEARNING FOR PHYSICS [PHYS-01/A] [ENG] | 1st | 2nd | 6 |
Educational objectives GENERAL OBJECTIVES:
Acquire familiarity with advanced deep learning techniques based on differentiable neural network models with supervised, unsupervised and reinforced learning paradigms; acquire skills in modelling complex problems through deep learning techniques, and be able to apply them to different application contexts in the fields of physics and basic and applied scientific research.
Discussed topics include: general machine learning concepts, differentiable neural networks, regularization techniques. Convolutional neural network, neural network for sequence analysis (RNN, LSTM / GRU, Transformers). Advanced learning techniques: transfer learning, domain adaptation, adversarial learning, self-supervised and contrastive learning, model distillation.
Graph Neural Networks (static and dynamic) and application to structured models for physics: dynamic models, simulation of complex fluids, GNN Hamiltonians and Lagrangians. Generative and variational models: variational mean-field theory, expectation maximization, energy based and maximum entropy models (Hopfield networks, Boltzman machines and RBM), AutoEncoders, Variational AutoEncoders, GANs, Autoregressive flow models, invertible networks, generative models based on GNN. Quantum Neural Networks.
SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) Knowledge of the functioning of neural networks and their mathematical interpretation as universal approximators
OF 2) Understanding of the limits and potential of advanced machine learning models
OF 3) Understanding of the limits and potential of DL in solving physics problems
B - Application skills
OF 4) Design, implementation, commissioning and analysis of deep learning architectures to solve complex problems in physics and scientific research.
C - Autonomy of judgment
OF 5) To be able to evaluate the performance of different architectures, and to evaluate the generalization capacity of the same
D - Communication skills
OF 6) Being able to clearly communicate the formulation of an advanced learning problem and its implementation, its applicability in realistic contexts
OF 7) Being able to motivate and to evaluate the generalization capacity of a DL model
E - Ability to learn
OF 8) Being able to learn alternative and more complex techniques
OF 9) Being able to implement existing techniques in an efficient, robust and reliable manner
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| 10625376 | GENERATIVE ARTIFICIAL INTELLIGENCE [IINF-05/A] [ENG] | 1st | 2nd | 6 |
Educational objectives General Objectives
At the end of the course, students will have a solid understanding and practical ability in the field of Generative AI, essential for tackling and solving complex problems in generative artificial intelligence.
Specific Objectives
Knowledge and Understanding:
Acquire an in-depth understanding of the principles behind image and text generation.
Learn the structures and mechanisms of generative models based on diffusion techniques and autoregressive techniques.
Critical Thinking and Judgment Skills:
Critically evaluate the performance of generative AI models and how they are used in real-world scenarios.
Analyze the challenges related to robustness in generative AI models and develop effective solutions.
Communication Skills:
Present and discuss the results of generative AI projects, demonstrating proficiency in the use of advanced tools such as Diffusion Models and Transformers.
Learning Skills:
Experiment with emerging technologies in the field of deep learning, such as LLMs, Vision LMs, Diffusion Models, Flow-based Models, etc.
Apply theoretical knowledge in practical projects to tackle real-world problems.
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| 10626114 | Deep Learning and Applied Artificial Intelligence [INFO-01/A] [ENG] | 1st | 2nd | 6 |
Educational objectives
General goals:
Familiarity with advanced machine learning techniques, both supervised and unsupervised; modeling skills of complex problems using deep learning techniques, and their application to diverse applicative settings.
Specific goals:
Topics include: deep neural networks, their training and the interpretation of results; convolutional networks and prominent architectures; theory of deep learning and convergence; programming frameworks for implementing advanced machine learning techniques; autoencoders; adversarial attacks.
Knowledge and understanding:
How neural networks work and their mathematical interpretation as universal approximators. Understanding the limits and potentials of advanced machine learning models.
Applying knowledge and understanding:
Design, implementation, deployment and analysis of deep learning architectures addressing complex problems in several applicative areas.
Critical and judgmental abilities:
To be able to evaluate the performance of different architectures, and to assess their generalization capabilities.
Communication skills:
To be able to communicate clearly how to formulate an advanced machine learning problem as well as its implementation, its applicability in realistic settings, and specific architectural and regularization choices.
Ability to learn:
Understanding alternative and more complex techniques such as generative models based on optimal transportation, scattering transforms and the energetic profile of neural networks. To be able to implement existing techniques efficiently, robustly and reliably.
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