STAGE Domain adaptation with Physics-informed neural networks

Context:
For decades, statistical or machine learning methods have been already applied successfully in many scientific and technical fields. However, their application to engineering science remain limited because of the lack of data and the difficulty in incorporating physical knowledge of systems into the models. Considering small data regime, researchers and engineers are turning more and more into hybrid models that combines approaches based on the knowledge of physics of the systems and also the data.
Recently, there has been a growing number of researches using deep learning methods to study physical systems, which are often described by partial differential equations (PDEs), by enforcing physical constraints into models. In this work, we focus on Physics-informed neural networks (PINNs) and their variants, which are recently proposed methods for solving forward and inverse problems involving PDEs and has gained remarkable results in different fields of research since the last two years.

Mission:
The main objective of this internship is to investigate in the use of PINNs on problems with geometric variations. In the first stage of the internship, the student will study the state-of-the-art of PINNs and existing methods concerned about domain adaptation. In the second stage, the student will develop appropriate approach for PINNs using domain adaptation methods to tackle the problems with geometric variations. In the final stage, the developed method will be applied to industrial use cases.