Stay flexible, get lucky: nonlinear approximation and random sampling meet scientific machine learning

Nonlinear approximation and random sampling are two vital mathematical pillars of machine learning. On the one hand, nonlinear approximation provides flexible models, such as sparse polynomials or deep neural networks, able to accurately represent very complex functions. On the other hand, random sampling allows us to solve data-starved inverse problems via, e.g., compressive sensing. In recent years, these tools have been frequently employed to tackle challenging problems in scientific computing within the research field now known as scientific machine learning.

In this talk, I will review recent advances in this area by showcasing results in high-dimensional approximation, surrogate modelling, data-driven discovery of dynamical systems and PDE solvers. Throughout the talk, the emphasis will be on numerical techniques accompanied by rigorous mathematical guarantees of performance.

Contatto:
marco.verani@polimi.it