Plenary Talks

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.

will talk about computational methods applied to biomedicine and medical imaging

will talk about development of solvers for large and ill-conditioned linear systems

will talk about models and simulation of extreme events and fluid structure interaction

will talk about Projection-free Methods for challenging Machine Learning Applications.