[Dottorcomp] PAV-IA seminars Reminder - Prof. Santiago Badia on " Adaptive finite element interpolated neural networks"

[Siam Student Chapter]

Dear all,

This is a gentle reminder about *today's* Seminar of PAV-IA, *from 15.00 to
16.00 *at the Department of Mathematics in Aula Beltrami, *followed by a
coffee break*.

This is the closing lecture of this year's PAV-IA seminars. PAV-IA will
resume in September/October, so stay tuned!

*Upcoming Seminar:*

   - *Title: * Adaptive finite element interpolated neural networks


   - *Speaker*:  Prof. Santiago Badia (Monash University)
   <https://research.monash.edu/en/persons/santiago-badia>


   - *Abstract*: We propose a general framework for solving forward and
   inverse problems constrained by partial differential equations, where we
   interpolate neural networks onto adaptive finite element spaces to
   represent the (partial) unknowns, and define loss functions with dual norms
   of the finite element residual of the interpolation. The framework
   overcomes the challenges related to the imposition of boundary conditions,
   the choice of collocation points in physics-informed neural networks, and
   the integration of variational physics-informed neural networks. We
   consider approximated dual norms (using multigrid methods) to accelerate
   the training process. A numerical experiment set confirms the framework's
   capability of handling various forward and inverse problems. In particular,
   the trained neural network generalises well for smooth problems, beating
   finite element solutions by some orders of magnitude in some cases. We
   finally propose an effective one-loop solver with an initial data fitting
   step (to obtain a cheap initialisation) to solve inverse problems. We will
   consider extensions to problems with complex geometries (using unfitted
   techniques) and problems posed in H(curl) and H(div).


   - *Where and when: *Tuesday, ORARIO  , at the Aula Beltrami, Department
   of Mathematics, University of Pavia.

*If you haven't already done so, please fill out this short form
<https://docs.google.com/forms/d/1-kH0a4VIVMZLOzGN0CHFN4Bi6A861IPLv8-9wN3Vk6c/edit>
to attend.*

We look forward to your participation!

Stay updated on SIAM Chapter activities by visiting our website
<https://sites.google.com/view/siam-unipv/home>.

Sincerely,
Luca and Massimiliano