The Assignment

An continuously growing field of research which alleviates the common problems of machine learning (ML) in computational fluid dynamics (CFD) are physics-informed neural networks (PINNs). In general, classical PINNs are specifically suited for smooth problems and suffer from stability problems if discontinuities are present in the solution. This is the case in many real applications such as transonic flows. Recently, modified versions of classical PINNs such as neural operators have been proposed to push their limitations and to enable PINNs which are more tailored to CFD.
The aim of this work is to investigate the potential of neural operators and compare their performance to classical PINNs for standard hyperbolic conservation laws.
To this goal, the research can be strutured as follows:

• Literature review on neural operators
• Compare neural operators to classical PINNs, starting with the Burgers equation and progessing to the Euler equations