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The event was organised by CMM researchers from the U. de Chile and CI²MA of the UdeC and included talks by academics from the PUCV.
On Thursday 6th, at the Faculty of Physical and Mathematical Sciences of the University of Concepción (UdeC), the seminar Combining Galerkin schemes and neural networks to solve partial differential equations was held, organized by the academic of that department and researcher of the Center for Mathematical Modeling (CMM) of the University of Chile, Dr. Manuel E. Solano.
The speakers of the seminar were two academics from the Institute of Mathematics of the Pontifical Catholic University of Valparaíso: Dr. Sergio Rojas Hernández and Dr. Ignacio Muga Urquiza, and their presentations were complementary to the Colloquium of the Department of Mathematical Engineering of the UdeC that took place earlier that same day, whose talk was given by the researcher from the University of Krakow AGH Paweł Maczuga.
Ignacio Muga and Sergio Rojas
Dr. Solano, also a member of the Center for Research in Mathematical Engineering, CI²MA, at UdeC, explained that “originally, Pawel was going to come to WONAPDE 2024, but for health reasons he had to postpone the trip. So a couple of months ago his mentor wrote to me so that Pawel could visit CI²MA and we could explore collaborative topics together.”
New techniques for better solutions
“Although I do not work directly on his research topic, which is related to Neural Networks to solve partial differential equations (PDEs),” Solano explained, “I found it interesting to learn what he does to apply these techniques to our problems. In this same direction, Sergio Rojas and Ignacio Muga, as far as I know, are the only researchers in Chile working on this topic. That is why I invited them, to enrich the discussions we have had during the week.”
Robust Variational Physics Informed Neural Networks is the title of the talk given by Rojas. In it, the PUCV researcher explains, “I presented a new methodology to define robust cost functionals based on a neural network approximation technique known as Variational Physics-Informed Neural Networks”.
“The main objective of this visit,” explains Dr. Rojas, “was to visit CI²MA in search of starting collaborations with professors Manuel Solano and Gabriel Gatica, in addition to continuing an existing collaboration with Dr. Julio Careaga”.
Meanwhile, his colleague Ignacio Muga presented ‘Neural Control of Discrete Weak Formulations of PDEs‘ and explained that “with Sergio and Pawel we are collaborating to solve equations using finite elements, which is what is basically done here, in addition to finite volumes, but we are also introducing neural networks, which are behind everything that is artificial intelligence, machine learning and that is, basically, what we came to show”.
In his talk, Muga presented on “how to enhance a finite element method using neural networks, for example, if you find the solution to a differential equation in a discrete approximation of the differential equation and you are not 100% satisfied, you want to improve certain attributes of the discrete solution, then we devise a way of how to do it by introducing a control that is based on a neural network”.
By Iván R. Tobar Bocaz, CMM journalist in Concepción.
Posted on Jul 4, 2024 in Noticias en castellano
