Applied Mathematics

Theory lectures [50% of the course hours] General recalls on differentiable artificial neural networks and use of the pytorch library for ANN design, training and testing. Basic architectures: MLP, Convolutional neural network, neural network for sequence analysis (RNN, LSTM / GRU). Bayesian-NN. Attention, Self-Attention, Transformers and Visual Transformers. Advanced learning techniques: transfer learning, domain adaptation, adversarial learning, self-supervised and contrastive learning, model distillation. Models for Object detection and semantic segmentation and applications. Graph Neural Network and Geometrical Deep Learning. Unsupervised models and anomaly detection. Generative Deep Learning: autoregressive models, invertible networks: diffusion and normalizing flow, generative GNN. Quantum Machine Learning on near-term quantum devices, design and training of quantum neural networks, Reinforcement Learning, Uncertainty quantification in DNNs. Energy models: Associative memories, Boltzmann Machines and RBMs. Computational hands-on sessions [50% of the course hours] Hands-on implementation and applications with Tensorflow and pytorch of the different models to physics problems.

important: calculus, linear algebra, basic notions of statistical and quantum mechanics. Essential: basics of machine learning and deep neural networks, good knowledge of the python language programming and use of the numpy, matplotlib, sklearn pandas, and pytorch libraries

Given the highly dynamic nature of the area covered by this advanced course, there is no single reference text. During the course the sources will be indicated and provided from time to time in the form of scientific articles and book chapters.

The course is constituted for about 50% of lectures supported by slides projections and exercises aimed at providing advanced knowledge of Deep Learning techniques. The remaining 50% is based on hands-on computational experiences that will provide the practical skills needed to develop and implement advanced Deep Learning models able to solve different problems in the field of physics and scientific research in general.

Attendance to the lectures is not mandatory but strongly recommended. Attendance to the laboratory activities is mandatory for at least 2/3 of the sessions

to pass the course it is necessary to develop and document an individual project assigned at the end of May to be delivered before the exam in which you wish to participate. During the exam session the student will be asked to present and discuss the project through a short presentation with slides (~15-20 min max), answering specific questions posed by the exam commission final grade is given by a weighted average between the vote on the project (50%) and the presentation and discussion (50%) To achieve a score of 30/30 cum laude, the student must demonstrate that he has acquired an excellent knowledge of the topics covered in the course, and to be able to master the software tools needed to develop and implement the computational model treated during the course. The determination of the final grade takes into account the following elements: 1. Home project 50% The project will be dimensioned in such a way that it requires a maximum of 2 weeks of work to be completed and documented (a written report of maximum 15 pages + code and dataset is required to reproduce the results reported in the report). It will consist in reproducing and possibly improving the results reported in a scientific article in which DL methods are applied to an interesting and accessible problem for the student. The evaluation will take into account: - Correctness of the concepts exposed; - Clarity of presentation; - Ability to elaborate the concepts learned in the development of original projects. 2. Presentation and discussion 50% The evaluation will take into account: - Correctness of the concepts exposed and of the answers to specific questions posed by the exam commission; - Clarity of presentation;

Reference texts: I. Goodfellow, Y. Bengio, A. Courville: Deep Learning, MIT Press (https://www.deeplearningbook.org/) P. Baldi, Deep Learning in Science, Cambridge University Press W. L. Hamilton, Graph Representation Learning Book, MCGill Uni press (https://www.cs.mcgill.ca/~wlh/grl_book/files/GRL_Book.pdf) M.Schuld, F.Petruccione, Machine Learning with Quantum Computers, Springer

The course is constituted for about 50% of lectures supported by slides projections and exercises aimed at providing advanced knowledge of Deep Learning techniques. The remaining 50% is based on hands-on computational experiences that will provide the practical skills needed to develop and implement advanced Deep Learning models able to solve different problems in the field of physics and scientific research in general.

Theory lectures [50% of the course hours] General recalls on differentiable artificial neural networks and use of the pytorch library for ANN design, training and testing. Basic architectures: MLP, Convolutional neural network, neural network for sequence analysis (RNN, LSTM / GRU). Bayesian-NN. Attention, Self-Attention, Transformers and Visual Transformers. Advanced learning techniques: transfer learning, domain adaptation, adversarial learning, self-supervised and contrastive learning, model distillation. Models for Object detection and semantic segmentation and applications. Graph Neural Network and Geometrical Deep Learning. Unsupervised models and anomaly detection. Generative Deep Learning: autoregressive models, invertible networks: diffusion and normalizing flow, generative GNN. Quantum Machine Learning on near-term quantum devices, design and training of quantum neural networks, Reinforcement Learning, Uncertainty quantification in DNNs. Energy models: Associative memories, Boltzmann Machines and RBMs. Computational hands-on sessions [50% of the course hours] Hands-on implementation and applications with Tensorflow and pytorch of the different models to physics problems.

important: calculus, linear algebra, basic notions of statistical and quantum mechanics. Essential: basics of machine learning and deep neural networks, good knowledge of the python language programming and use of the numpy, matplotlib, sklearn pandas, and pytorch libraries

Given the highly dynamic nature of the area covered by this advanced course, there is no single reference text. During the course the sources will be indicated and provided from time to time in the form of scientific articles and book chapters.

The course is constituted for about 50% of lectures supported by slides projections and exercises aimed at providing advanced knowledge of Deep Learning techniques. The remaining 50% is based on hands-on computational experiences that will provide the practical skills needed to develop and implement advanced Deep Learning models able to solve different problems in the field of physics and scientific research in general.

Attendance to the lectures is not mandatory but strongly recommended. Attendance to the laboratory activities is mandatory for at least 2/3 of the sessions

to pass the course it is necessary to develop and document an individual project assigned at the end of May to be delivered before the exam in which you wish to participate. During the exam session the student will be asked to present and discuss the project through a short presentation with slides (~15-20 min max), answering specific questions posed by the exam commission final grade is given by a weighted average between the vote on the project (50%) and the presentation and discussion (50%) To achieve a score of 30/30 cum laude, the student must demonstrate that he has acquired an excellent knowledge of the topics covered in the course, and to be able to master the software tools needed to develop and implement the computational model treated during the course. The determination of the final grade takes into account the following elements: 1. Home project 50% The project will be dimensioned in such a way that it requires a maximum of 2 weeks of work to be completed and documented (a written report of maximum 15 pages + code and dataset is required to reproduce the results reported in the report). It will consist in reproducing and possibly improving the results reported in a scientific article in which DL methods are applied to an interesting and accessible problem for the student. The evaluation will take into account: - Correctness of the concepts exposed; - Clarity of presentation; - Ability to elaborate the concepts learned in the development of original projects. 2. Presentation and discussion 50% The evaluation will take into account: - Correctness of the concepts exposed and of the answers to specific questions posed by the exam commission; - Clarity of presentation;

Reference texts: I. Goodfellow, Y. Bengio, A. Courville: Deep Learning, MIT Press (https://www.deeplearningbook.org/) P. Baldi, Deep Learning in Science, Cambridge University Press W. L. Hamilton, Graph Representation Learning Book, MCGill Uni press (https://www.cs.mcgill.ca/~wlh/grl_book/files/GRL_Book.pdf) M.Schuld, F.Petruccione, Machine Learning with Quantum Computers, Springer

The course is constituted for about 50% of lectures supported by slides projections and exercises aimed at providing advanced knowledge of Deep Learning techniques. The remaining 50% is based on hands-on computational experiences that will provide the practical skills needed to develop and implement advanced Deep Learning models able to solve different problems in the field of physics and scientific research in general.