Error Estimates for Finite Element Simulations Using Neural Networks

Bachelor thesis (2022)

Authors

A.L. Halevy Electrical Engineering, Mathematics and Computer Science

Contributors

A. Heinlein Numerical Analysis - (mentor)

D. Toshniwal Numerical Analysis - (mentor)

D.J.P. Lahaye Mathematical Physics - (graduation committee member)

Faculty

Electrical Engineering, Mathematics and Computer Science, Electrical Engineering, Mathematics and Computer Science

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

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

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Published Date

19-07-2022

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

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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