Seminar in EDP and Applied Mathematics

April 16 , 2025 – 14h (Brazil)

Streaming: Youtube Channel | SEMINARIO DE EDP E MATEMATICA APLICADA

Event

About Seminars

Our Online Seminar is one of the most important events in Brazil, it has been held since August 2020, every Wednesday at 2 pm, Brasília time, with a frequency of 14 days. Two 40-minute lectures are presented in each session. Our speakers are world-renowned mathematicians from Europe, the United States and South America.

Featured Talks & Speakers

Alessio Figalli

ETH Zurich | Department of Mathematics,Switzerland

14:00h – 14:40h

Free boundary regularity for the obstacle problem

The classical obstacle problem consists of finding the equilibrium position of an elastic membrane whose boundary is held fixed and constrained to lie above a given obstacle

By classical results of Caffarelli, the free boundary is smooth outside a set of singular points. However, explicit examples show that the singular set could be, in general, as large as the regular set. This talk aims to introduce this beautiful problem and describe some classical and recent results on the regularity of the free boundary.

Fabio Ramos

Universidade Federal do Rio de Janeiro,Brazil

14:50h – 15:30h

Controlled Latent Diffusion Models for 3D Porous Media Reconstruction

Inverse problems are pivotal in porous media analysis, demanding the reconstruction of subsurface microstructures from limited imaging data—critical for applications such as energy exploration, hydrocarbon recovery, and underground storage. While traditional approaches often rely on statistical or physics-based models, recent breakthroughs in deep generative methods—particularly diffusion-based approaches—present new avenues for enhanced accuracy and computational efficiency.

In this talk, I will introduce a novel framework for reconstructing 3D porous microstructures using controlled latent diffusion models, developed in collaboration with ExxonMobil. By integrating the EDM diffusion framework with a tailored variational autoencoder (VAE), we achieve high-resolution digital rock reconstructions while preserving computational feasibility. Furthermore, we propose controlled unconditional sampling, an approach that improves model reliability through the incorporation of physical constraints such as porosity and two-point correlation functions.

Our results demonstrate that generative models can act as powerful, data-driven solvers for inverse problems, addressing challenges where traditional physics-based models falter due to data scarcity or high computational costs. This methodology is broadly applicable across geophysics, medical imaging, and materials science—any field where reconstructing complex microstructures from indirect observations is essential.

This work is in collaboration with Danilo Naiff (UFRJ), Bernardo P. Schaeffer (UFRJ), Gustavo Pires (UFRJ), Dragan Stojkovic(ExxonMobil) and Thomas Rapstine (ExxonMobil).

About Organization

Juan Limaco -UFF-Coordenador
Mauro Rincon – UFRJ – Brazil
Anna Doubova-U.Sevilla-Spain

Luz de Teresa-UNAM Mexico

Diego Souza – U Sevilla -Spain

Felipe Chaves-UFPB-Brazil

Roberto Capistrano – UFPE Brazil
Sandra Malta – LNCC – Brazil
Eduardo Cerpa – U.C – Chile
Giovani Figueiredo – UNB – Brazil
Marcia Federson USP,San Carlos –Brazil;
Maicon Correa – UNICAMP- Brazil