Alfio Maria Quarteroni: Physics-Informed and Data-Driven Models for Solving Partial Differential Equations II

Abstract for lectures 2 and 3

Recent advances in artificial intelligence have produced impressive results across a wide range of applications, yet significant concerns remain regarding accuracy, uncertainty quantification, and the opacity of AI models—often criticized as “black boxes.” Scientific Machine Learning (SciML) emerges as a compelling paradigm by combining data-driven methods with models grounded in physical laws, thus fostering a transparent and interpretable framework that bridges AI and traditional scientific approaches.

In the first of these two lectures, we will delve into the mathematical foundations of machine learning, examining core algorithms, theoretical properties, and their limitations.

The following lecture will be dedicated to Scientific Machine Learning, with a particular focus on operator learning strategies for the numerical resolution of partial differential equations. This approach demonstrates how physical constraints and data can be harmoniously integrated to enhance the reliability and performance of numerical solvers.

See webpage  for more information.