Machine learning enhanced finite elements
Titus Ex

Supervisor TU Delft: Deepesh Toshniwal

start of the project: July 2020

In February 2021 the Interim Thesis has appeared and a presentation has been given.

The Master project has been finished in December 2021 by the completion of the Masters Thesis and a final presentation has been given.

For working address etc. we refer to our alumnipage.

Summary of the master project:
Scientific machine learning (ML) for solving partial differential equations has become increasingly popular over the last few years. The reasons for this are the benefits afforded by two complementary points of view:

(a) swapping conventional numerical methods our with ML (e.g., physics-informed neural networks [1]) leading to drastically reduced simulation times,

(b) enhancing conventional numerical methods with ML (e.g., for tuning algorithmic parameters [2]) leading to accelerated, heuristic-free methods with increased generality. This project will focus on the latter point of view in the context of the finite element method. In particular, the project will investigate the use of generative ML for the construction of stable finite element discretizations.

[1] Raissi, Maziar, Paris Perdikaris, and George E. Karniadakis. "Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations." Journal of Computational Physics 378 (2019): 686-707.

[2] Discacciati, Niccolo, Jan S. Hesthaven, and Deep Ray. "Controlling oscillations in high-order Discontinuous Galerkin schemes using artificial viscosity tuned by neural networks." Journal of Computational Physics (2020): 109304.

Contact information: Kees Vuik

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