Speaker: Juan Pablo Borthagaray (Instituto de Matemática y Estadística, Facultad de Ingeniería, Universidad de la República, Montevideo, Uruguay)
Title: A deep learning-based FOSLS method for second-order elliptic PDEs.
Time: Wednesday, 2023.09.20, 2:00 p.m. (CET)
Place: fully virtual (contact Jakub Lengiewicz to register)
Abstract: We present a First-Order System Least Squares (FOSLS) method based on deep learning for the numerical solution of second-order elliptic PDEs. The method we propose can handle both variational and non-variational problems. Due to its meshless nature, it is also suitable for tackling problems in high-dimensional domains. We prove the Γ-convergence of the neural network approximation towards the solution of the continuous problem. Furthermore, we extend the convergence proof to encompass several well-known related methods. Finally, we provide several numerical examples that illustrate the performance of the method.
Juan Pablo Borthagaray is an associate professor at Instituto de Matemática y Estadística, Facultad de Ingeniería, Universidad de la República in Uruguay. He obtained his PhD in Mathematics from the Universidad de Buenos Aires in 2017. His research area lies between the numerical analysis and the analysis of partial differential equations (PDEs). This includes mainly finite element methods, the analysis and design of numerical methods for nonlocal operators and the study of certain geometric PDEs.
Additional material:
Francisco M. Bersetche, Juan Pablo Borthagaray, A deep First-Order System Least Squares method for solving elliptic PDEs, Computers & Mathematics with Applications, vol. 129, pp. 136-150, 2023
The aim of the Machine Learning Seminar series is to host presentations on fundamental and methodological advances in data science and machine learning, as well as to discuss application areas presented by domain specialists. The uniqueness of the seminar series lies in its attempt to extract common denominators between domain areas and to challenge existing methodologies. Therefore, the focus is on theory and applications to a wide range of domains, including Computational Physics and Engineering, Computational Biology and Life Sciences, and Computational Behavioural and Social Sciences. The seminar aims to bring together young and experienced researchers from various disciplines to exchange ideas on Machine Learning techniques. It is currently affiliated with the University of Luxembourg and is run under the auspices of the DTU DRIVEN PRIDE project, funded by the FNR, and the widening participation DRIVEN project, funded by H2020. The seminar also welcomes talks by researchers from a wider collaborative network, including but not limited to early-stage researchers in RAINBOW ITN, as well as current and incoming individual Marie Skłodowska-Curie fellows.
The usual format is as follows: a short presentation (20-30 minutes) followed by a longer discussion (30-40 minutes). The usual time is Wednesdays at 10:00 a.m. (CET). If you are interested in joining, please contact Jakub Lengiewicz. See www.jlengineer.eu/ml-seminar/.
20 сен 2023
