4. Conclusions and outlook

This study highlights the use of RNs to couple a solution of an equation describing the physics of a problem with, in practice, experimental data (data from known solutions in this study). When the links between the functions sought and the data are non-linear, an RN is considered in order to adequately describe this link. In this article, the PINN and PCL methods are illustrated both theoretically and numerically. PINN can be designed to solve either direct or inverse problems; in the context of a direct problem, its advantage is that it can couple data with the solution of a differential equation. However, the choice of coupling data and equation introduces a further difficulty in minimizing the loss function. PCL is designed to solve inverse problems with data at hand, and its advantage is that minimization of the RN, based on a loss function with a single contribution on the data, is...