[Dottorcomp] Reminder: inaugural lecture of the PAV-IA seminars

[Siam Student Chapter]

Dear all,

This is a gentle reminder about the inaugural lecture of the PAV-IA
seminars  which will be held *Today from 14:30 to 15:30,* at the Department
of Mathematics in Aula Beltrami.

*Lecture Details:*

*    Speaker:  *

Francesco Regazzoni <https://regazzoni.faculty.polimi.it/> Politecnico di
Milano

*    Title:  *

Integrating physics-based models with machine learning for fast and
accurate simulations

*    Abstract: *

Mathematical models based on differential equations, such as Partial
Differential Equations (PDEs) and Stochastic Differential Equations (SDEs),
can yield quantitative predictions of physical processes. However, model
development requires a deep understanding of the physical processes, that
is not always available. Furthermore, the computational cost that
accompanies the (possibly many-query) numerical approximation of such
mathematical models may be prohibitive and hinder their use in relevant
applications. In this talk, we present scientific machine learning methods
that integrate physical knowledge with data-driven techniques to accelerate
the evaluation of differential models and address many-query problems -
such as sensitivity analysis, robust parameter estimation, and uncertainty
quantification. To speed up input-output evaluations, we present Universal
Solution Manifold Networks <https://arxiv.org/pdf/2204.07805>, namely
emulators of differential models capable of predicting spatial outputs and
accounting for the variability of the computational domain. Our method is
based on a mesh-less architecture, thus overcoming the limitations
associated with image segmentation and mesh generation required by
traditional discretization methods, and encodes geometrical variability
through an automatic shape encoding technique. Furthermore, we present Latent
Dynamics Network <https://www.nature.com/articles/s41467-024-45323-x>, a
space-time operator-learning method, which shows, tested in challenging
problems, superior accuracy (normalized error 5 times smaller) with
significantly fewer trainable parameters (more than 10 times fewer) than
state-of-the-art methods. Numerical results demonstrate that these
scientific machine learning methods enhance efficiency and accuracy in
approximating quantities of interest, as well as in solving parameter
estimation and uncertainty quantification problems.


We look forward to your participation!

Sincerely,

PAV-IA Organizing Committee