Algebraic flux correction enhanced by scientific machine learning
Sannia Ul Haq
Supervisors TU Delft: Matthias Moller and Deepesh Toshniwal
start of the project: June 2021
The Master project has been finished in August 2022
by the completion of the
and a final
has been given.
For working address etc. we refer to our
Summary of the master project:
Numerical methods like finite elements and finite volumes are known to become unstable for convection-dominated problems which manifests itself in the creation of spurious oscillatory in the vicinity of steep gradients and shocks, which in turn leads to unphysical behaviour and, in the worst case, the crash of the simulation. Stabilisation techniques like the algebraic flux correction approach are a reliable cure. However, the various AFC schemes all require some extra calculations to determine the optimal amount of stabilising artificial diffusion and, moreover, are based on worst-case scenario analysis. As a result the formula-based limiters are often overly pessimistic and add too much artificial diffusion. This project will explore the possibilities to learn the behaviour of the limiters with the aid of neural networks so that the time-consuming extra calculations can be replaced by a computationally cheap evaluation of the neural network. Secondly, we will investigate if the so-trained neural network can be improved beyond the capabilities of the formula-based limiter, e.g., to distinguish between "harmless" local extrema that do not need any further treatment and those that call for the addition of stabilising artificial diffusion.
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