Strategies for approximating the solutions of partial differential equations by means of Neural Networks have recently gained in popularity. These so-called Physics-Informed Neural Networks (PINNs) are issued from recent advances in the field of Artificial Intelligence and bring a new paradigm compared to conventional numerical methods such as Finite Volume or Finite Element Methods. The core of the method consists in enforcing the physical model thanks to the loss function by minimizing the residual of the operators. Although these methods show promising results on academic problems, they also bring many specific questions regarding their benefits for complex applications and their mathematical properties. The present Ph.D proposal aims at studying both aspects.
The candidate will first perform a state of the art study in order to understand the PINNs approach and their potential as a industrial grade simulation method. We propose then to focus on several problems involving different types of complexity issued from physical processes applications like the two-phase flows or the coupling of neutronics and thermal-hydraulics.