<div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div>Dear all,</div><div><div><div><p>This
is a gentle reminder about the <font size="2" style="color:rgb(0,0,0)">inaugural lecture of the PAV-IA seminars </font><font size="2" style="color:rgb(0,0,0)">
which will be held <b>Today from 14:30 to 15:30,</b> </font>at the Department of Mathematics in Aula Beltrami.</p><div><div dir="ltr"><font size="2" style="color:rgb(0,0,0)"><br></font></div><div style="text-align:center"><font size="4" style="color:rgb(0,0,0)"><u><b>Lecture Details:</b></u></font></div><div style="text-align:center"><font size="2" style="color:rgb(0,0,0)"><u><b><br></b></u></font></div><div style="text-align:center"><font size="4" style="color:rgb(0,0,0)"><b> Speaker: </b><b><br></b></font></div><div style="text-align:center"><font size="2" style="color:rgb(0,0,0)"><b><br></b></font></div><div dir="ltr"><div style="text-align:center"><font size="2" style="color:rgb(0,0,0)"><a href="https://regazzoni.faculty.polimi.it/" rel="noreferrer" target="_blank">Francesco Regazzoni</a> </font><span>Politecnico di Milano</span></div><div style="text-align:center"><font size="2" style="color:rgb(0,0,0)"><b> </b></font></div><div style="text-align:center"><font size="4" style="color:rgb(0,0,0)"><b> Title: </b></font></div><div style="text-align:center"><font size="2" style="color:rgb(0,0,0)"><br></font></div><div style="text-align:center"><font size="2" style="color:rgb(0,0,0)">Integrating physics-based models with machine learning for fast and accurate simulations<br><br></font><font size="4" style="color:rgb(0,0,0)"><b> Abstract: </b><br></font></div><div style="text-align:center"><font size="2" style="color:rgb(0,0,0)"><br></font></div><div style="text-align:center"><div style="text-align:left"><div style="text-align:left"><font size="2" style="color:rgb(0,0,0)">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 <a href="https://arxiv.org/pdf/2204.07805" target="_blank">Universal Solution Manifold Networks</a>, 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 <a href="https://www.nature.com/articles/s41467-024-45323-x" target="_blank">Latent Dynamics Network</a>, 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.<br></font></div><font size="2" style="color:rgb(0,0,0)"><b><br><br></b></font></div></div></div><p>We look forward to your participation!</p></div></div><div><div></div></div></div><div><div><div><div><p><span>Sincerely,</span><span> </span></p><p><font size="2" style="color:rgb(0,0,0)">PAV-IA Organizing Committee</font></p></div></div></div></div></div></div></div></div></div></div></div></div></div>
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