The course will alternate between theoretical lectures and hands-on sessions (held in Python), in which the students will become familiar with the topics through a learning-by-doing approach

The first part of the course will provide a review of the basic concepts of machine learning, including backpropagation, automatic differentiation, the notion of model capacity and overfitting, the bias-variance trade-off, regularization techniques. An overview on training algorithms (stochastic gradient descent, momentum methods, learning rate adaptivity, second-order methods) and of hyperparameters tuning methods will be provided as well. We will then focus on neural networks (NNs), with hints on the approximation theory of NNs in function spaces. The second part of the course will focus on Scientific Machine Learning. We will introduce surrogate modeling and operator learning techniques and motivate them through specific applications. Then, we will address physics-informed learning, including physics-informed neural networks (PINNs), for the solution of direct and of inverse problems associated with differential models.

In presenza

Sviluppo di project work in team

P.D.2-2 - Marzo