Error Estimates for Finite Element Simulations Using Neural Networks

Title

Error Estimates for Finite Element Simulations Using Neural Networks

 Author

Halevy, Avi (TU Delft Electrical Engineering, Mathematics and Computer Science; TU Delft Numerical Analysis)

Contributor

Heinlein, A. (mentor) ORCID 0000-0003-1578-8104
Toshniwal, D. (mentor) ORCID 0000-0002-7142-7904
Lahaye, D.J.P. (graduation committee)

Degree granting institution

Delft University of Technology

 Programme

Applied Mathematics

 Date

2022-07-19

 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.

 Subject

Transformers
Neural Network
Finite Element Method
Residual error estimates
Adaptive Mesh Refinement
Multilayer Perceptron
Differential Equations

 To reference this document use:

http://resolver.tudelft.nl/uuid:31084250-25ee-4901-a3f0-258a6436be29

 Part of collection

Student theses

 Document type

bachelor thesis

 Rights

© 2022 Avi Halevy
Files
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