A Comparison of Machine Learning and Classical Numerical Approaches for the Resolution of Electromagnetics Problems

Machine Learning (ML) approaches are getting increasingly common in numerical modelling, thanks to their promptness once trained and to their capability of self-extracting numerical models from behavioural examples. While classical numerical models have been developed for many years and presently represent a robust and well-known solution to handle complex electromagnetic (EM) models, they still suffer from some drawbacks—the need to create a discrete version of the model from basic laws and the need for massive computational power in more complex cases. Although commercial software tools have been developed that are able to handle semi-automatically these issues, in some applications, such as optimised design and iterative resolution of inverse problems, the cited issue may still represent a relevant limitation. We aim to balance the drawbacks and the advantages of both approaches, by investigating the performance of representative methods in each class on a simple yet relevant electrostatic problem described by Elliptic Partial Differential Equations (E-PDE).