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.

Clinical practice and research are deeply affected by information coming from medical imaging, thanks to both new scanners and new technologies, like the ones involved in the collection of omics data. In order to fully exploit the potentiality of medical images and omics data many computational approaches have been  developed, with the aim to improve treatment of diseases and to help physicians in their clinical choices. In this talk I will present an overview of computational methods for the processing of medical data.

It is very well-known that coupled poromechanical simulations play a crucial role for a proper management of underground resources, involving multiple physical processes, such as fluid flow, poromechanics, fault activation, thermal flow, and chemical reactions, that can take place simultaneously with multiple time and space scales. This presentation focusses on the development of GReS, a novel open-source modular platform specifically designed with the aim at contributing to the design and testing of numerical algorithms for fully coupled multi-physics multi-domain poromechanical applications. The idea is to partition the overall computational domain into possibly non-conforming subdomains where different physics and discretization schemes can be used. The different subdomains are connected by a modified mortar algorithm that can take into account the potential sliding and/or separation of the contact surfaces. The code is based on a high-level programming platform (MATLAB) that should lower the entry barrier for new users and developers, as well as the effort for implementing and testing innovative numerical algorithms. At the same time, GReS wraps low-level advanced linear algebra packages to combine simplicity with fair efficiency. 

In this presentation, we will introduce the GReS concept and its current development state, including the advances introduced to the mortar algorithm used to transfer the information among non-conforming subdomains with independent meshes. Several benchmarks will be presented to show the current code’s potentials, along with the projects for future developments.

Climate change poses significant threats to structures, landscapes, and human life, necessitating urgent scientific attention and effective mitigation strategies. In response, recent advances in computational techniques have emerged for simulating multiphysics phenomena, particularly in the context of large mass movements and natural hazards. 

We focus on developing and implementing innovative numerical formulations to accurately model complex interactions between water, air, particles, and soil in mountainous environments. Strategies for coupling different methods  are discussed to enhance versatility in multiphysics simulations, aiming to improve our understanding and prediction of these critical environmental processes.

This talk explores the use of projection-free algorithms, such as the Frank-Wolfe Method and its variants,

for optimization problems with structured constraints. We analyse both theoretical and computational properties of those methods. Additionally, we discuss some applications in, e.g.,  machine learning, and complex network analysis where the methods enable scalable and efficient solutions.