Khoa NGUYEN : soutenance de thèse

Khoa NGUYEN

Development and assessment of physics-informed deep learning methods: towards multiphysics simulation in industrial contexts

Résumé de la thèse

Physics-informed deep learning approaches have gained huge attention in various engineering fields for the last few years thanks to the capability of incorporating physical knowledge, which is often represented using Partial Differential Equations (PDEs), into deep learning models. The main idea of these approaches is to employ neural networks as approximators and integrate the physical constraints of the systems either into the cost function or into the network architecture. Among these approaches, Physics-Informed Neural Networks (PINNs) rise as an attractive and remarkable scheme of solving forward and inverse ill-posed PDEs problems using only a moderate amount of, or even without supervised data. In this thesis, we are interested in investigating PINNs to solve complex multiphysics problems. The first part of this thesis focuses on improving PINNs accuracy using adaptive strategies during the training on the unsupervised points (or collocation points) of PINNs. We propose a novel approach that is able to infer the best location of the training points based on the PDEs residuals. Different from other existing approaches, our proposed method aims to capture not only the global extrema but also the local extrema of the PDEs residuals, thus improving the accuracy and reducing the training time. We later demonstrate the effectiveness of our proposed method to improve PINNs accuracy in multiphysics fluid mechanics problems with physical couplings relevant to industrial contexts. In these practical scenarios, we encounter realistic test cases, including the rubber calendering process used in tire manufacturing and the interactions between boundary layers and mountains in atmospheric modeling. Through these applications, PINNs with our enhanced approach demonstrate their great capability of inferring the hidden physics from local measurements and identifying the unknown PDEs parameters. These tasks often prove challenging to classical numerical discretization methods. In the second part of the thesis, we investigate the geometry-aware frameworks for PINNs and propose a novel version for the deep energy PINNs-based method, which employs the weak form of the physical system equation and minimizes the loss function based on the potential energy of all considered geometries. It is expected that these geometry-aware frameworks can infer the solution on various shapes of geometry using only one trained model. We present the performance of our proposed approach to solve structural solid mechanics problems using different techniques for geometric representation and encoding. The effectiveness of our approach is also demonstrated in a complex hyperelastic problem related to an industrial toy tire loading simulation test case, where the model is successfully inferring the displacements of different tires after loading. The performance of the geometry-aware PINNs framework is later illustrated in a fluid mechanics problem involving the interactions between boundary layers and mountains on various mountain shapes. Lastly, we develop an open-source package and tutorials for PINNs that facilitate PINNs implementation. We illustrate the use of our proposed package in various tasks, including forward with either strong or weak formulations, inverse, ill-posed problems, and geometry-aware modeling. Besides that, difference enhancement techniques, such as the adaptive activation functions, adaptive training points, and adaptive weights in the loss function, are also implemented in the package. We note again that all the proposed approaches developed during this thesis have undergone various test cases including the realistic applications at Michelin and CEA involving complex physical problems.

Direction :

• Mathilde MOUGEOT
• Christophe MILLET
• Thibault DAIRAY

Jury :

• Taraneh Sayadi, Professeure (CNAM Paris), Rapporteure
• Patrick Gallinari, Professeur des universités (Sorbonne Université), Rapporteur
• Clémentine Prieur, Professeure des universités (Université Grenoble Aples), Examinatrice
• Florian De Vuyst, Professeur des universités (Sorbonne Université), Examinateur
• Didier Lucor, Directeur de recherche (LISN-CNRS), Examinateur
• Emmanuel Franck, Chargé de recherche (INRIA Nancy Grand-Est), Examinateur