Using a Physics-Informed Neural Network to solve the Ideal Magnetohydrodynamic Equations
J.F. Bouma (TU Delft - Electrical Engineering, Mathematics and Computer Science)
Matthias Möller – Mentor (TU Delft - Numerical Analysis)
Deepesh Toshniwal – Mentor (TU Delft - Numerical Analysis)
A. R. Akhmerov – Mentor (TU Delft - QN/Akhmerov Group)
Johan L.A. Dubbeldam – Mentor (TU Delft - Mathematical Physics)
S KenjereS – Mentor (TU Delft - ChemE/Transport Phenomena)
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Abstract
In this work we investigate neural networks and subsequently physics-informed neural networks. Physicsinformed neural networks are away to solve physical models that are based on differential equations by using a neural network. The wave equation, Burgers’ equation, Euler’s equation, and the ideal magnetohydrodynamic equations are introduced and solved with physics-informed neural networks. The solutions to the first equations were captured well. The solution to the ideal magnetohydrodynamic equations contained some problems. These problems include transitions between different types of behaviour and exact values of constant sections. On the other hand, general shape and behaviour of the curve and locations of contact discontinuities were predicted well.