Seminario IMC: Challenges when integrating neural networks for solving parametric PDEs
30 de Diciembre, 2025
El Instituto de Ingeniería Matemática y Computacional (IMC) invita al seminario que se dictará el miércoles 7 de enero.
Miércoles 7 de enero de 2025, 13:40 hrs. (Presencial en auditorio Edificio San Agustín. Link Zoom disponible escribiendo a imc@uc.cl)
ABSTRACT
This presentation examines the use of Physics-Informed Neural Networks (PINNs), Variational Physics-Informed Neural Networks (VPINNs), Deep Ritz methods, and First Order System Least Squares (FOSLS) combined with stochastic quadrature rules, to solve parametric partial differential equations (PDEs). It begins by introducing parametric PDEs and how these neural network techniques can be used to solve them. The presentation then delves into the challenges of solving these PDEs, including optimization, regularity, and integration. It points out that while PINNs using strong formulations may have trouble with singular solutions, they handle integration better than weak formulation methods like VPINNs or Deep Ritz. To address these integration challenges, we propose the use of unbiased high-order stochastic quadrature rules for better integration and Regularity Conforming Neural Networks to deal with complex solutions and singularities.
Finally, the presentation discusses the broader significance of this research for solving parametric PDE problems and suggests directions for future research, and how FOSLS and PINNs may work better than VPINNs and Deep Ritz in different cases.
BIO
David Pardo is a Research Professor at Ikerbasque, the University of the Basque Country UPV/EHU, and the Basque Center for Applied Mathematics (BCAM). He has published over 160 research articles and he has given over 260 presentations. In 2011, he was awarded as the best Spanish young researcher in Applied Mathematics by the Spanish Society of Applied Mathematics (SEMA). He leads a European Project on subsurface visualization, several national research projects, as well as research contracts with national and international companies. He is now the PI of the research group on Applied Mathematical Modeling, Statistics, and Optimization (MATHMODE) at UPV/EHU and co-PI of the sister research group at BCAM on Mathematical Design, Modeling, and Simulations (MATHDES).
His research interests include computational electromagnetics, petroleum-engineering applications (borehole simulations), adaptive finite-element and discontinuous Petrov-Galerkin methods, multigrid solvers, deep learning algorithms, and multiphysics and inverse problems.
