Parareal Physics-Informed Neural Networks for Transient Electromagnetic Field Problems

Type of work flexible, Master thesis, HiWi Position, Projectseminar, Bachelor thesis

Artificial Neural Networks (NNs) have provided transformative results in numerous and diverse engineering domains, e.g. image processing or pattern recognition. In recent years, NNs have also been utilized for solving Partial Differential Equations (PDEs). Therein, one of the most popular approaches are Physics-Informed Neural Networks (PINNs).

A major drawback of PINNs is the computational cost arising due to the use of large datasets and NNs with many degrees of freedom. As a remedy, a recent work has proposed a combination of the Parareal and PINN algorithms, resulting in a method referred as PPINN. The PPINN algorithm splits long-time problems into many independent short-time problems, supervised by an inexpensive and fast coarse-grained conjugatebgradient solver. The benefit of PPINN is that it decreases the computational cost of training a DNN by reducing the size of the training set and the number of d.o.f.s per network.

The task of the thesis is to implement the PPINN algorithm to a suitable, transient electromagnetics problem, a test case that has not appeared in the literature so far. A comparison against standard PINNs will complement this work.