Error Estimates for Finite Element Simulations Using Neural Networks

Bachelor Thesis (2022)
Author(s)

A.L. Halevy (TU Delft - Electrical Engineering, Mathematics and Computer Science)

Contributor(s)

Alexander Heinlein – Mentor (TU Delft - Numerical Analysis)

D Toshniwal – Mentor (TU Delft - Numerical Analysis)

D.J.P. Lahaye – Graduation committee member (TU Delft - Mathematical Physics)

Faculty
Electrical Engineering, Mathematics and Computer Science
Copyright
© 2022 Avi Halevy
More Info
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Publication Year
2022
Language
English
Copyright
© 2022 Avi Halevy
Graduation Date
19-07-2022
Awarding Institution
Delft University of Technology
Programme
['Applied Mathematics']
Faculty
Electrical Engineering, Mathematics and Computer Science
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Abstract

In this work residual error estimates are constructed using Neural Networks for Finite Element Method. These can be used to do adaptive mesh refinement. Two neural networks are developed the Multilayer Perceptron and the Transformer model. The error estimates are made for 1d poisson equations but the idea will generalise to higher dimensions as well.

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