IACM Colloquium
Seminar title:
Deep Ritz-PINNs: Neural Networks trained with Finite Elements
Speaker:
Georgios Grekas,
Assistant Professor,
Department of Mathematics
University of Ioannina
Abstract:
Over the past few years, neural network methods have evolved in various directions for approximating partial differential equations (PDEs). A promising new development is the integration of neural networks with classical numerical techniques such as finite elements and finite differences. In this work we suggest to connect finite elements and neural network approximations through training, i.e., using finite element spaces to compute the integrals appearing in the loss functionals. This approach, retains the simplicity of classical neural network methods for PDEs, uses well established finite element tools (and software) to compute the integrals involved and it gains in efficiency and accuracy. We demonstrate that the proposed methods are stable and furthermore, we establish that the resulting approximations converge to the solutions of the PDE. Numerical results indicating the efficiency and robustness of the proposed algorithms are presented.
Short CV:
Georgios Grekas is an Assistant Professor in the Department of Mathematics at the University of Ioannina. He received his Ph.D. in Applied Mathematics from the University of Crete in 2019. Part of his doctoral studies took place at the University of Sussex from March 2016 to March 2018. From 2019 to 2022, he held a postdoctoral position in the Department of Aerospace Engineering and Mechanics at the University of Minnesota. He then worked as a postdoctoral researcher at the Institute of Applied and Computational Mathematics (IACM) at FORTH, Greece. From March 2024 to March 2026, he served as a Postdoctoral Research Fellow in the Applied PDE Group at KAUST (King Abdullah University of Science and Technology). His research interests include mathematical modeling (biomechanics, solid mechanics), numerical analysis, scientific and parallel computing, and scientific machine learning.
Time, Date & Location:
15:00, October 29, 2026, Fotakis Room
Join Zoom Meeting
https://us06web.zoom.us/j/81621524841?pwd=snQ4Qx5oXx1lBRqL97MQird5SveIXu.1
Meeting ID: 816 2152 4841
Passcode: 828906