La fédération MIRES organise une journée thématique sur les Réseaux de neurones et leurs applications, notamment l’utilisation des PINNs  – Physics Informed Neural Networks

Cet évènement se déroulera le 28 mars 2024 à Poitiers (sous format hybride) – Amphithéâtre du Bâtiment B25 sur le campus sud de l’université de Poitiers.

Si vous souhaitez assister aux présentations en présentiel ou à distance, merci de compléter le formulaire suivant : https://evento.renater.fr/survey/reunion-du-28-mars-y0q6xduc

L’accès a distance se fera via webex à l’adresse suivante : https://univ-poitiers.webex.com/univ-poitiers-en/j.php?MTID=m8816f850160b0205164fbcd561c8d11c

Programme prévisionnel 

9h – 9h30 : Accueil

9h30 – 10h30 : Méthodes numériques: des approches de traditionnelles vers les méthodes neurales

Orateur : Emmanuel Franck

Depuis quelques années ont émergées plusieurs méthodes pour approcher les solutions d’EDP à l’aide de réseaux de neurones comme les PINNs, la méthode Neural Galerkin, ou les méthodes de réductions d’ordre continues. On se propose de montrer que ces méthodes peuvent être vue comme de nouvelles méthodes numériques très proches dans l’esprit des méthodes numériques usuelles, mais avec des qualités et des défauts très différents des techniques usuelles qu’on discutera.

10h30 – 11h : Pause

11h – 11h45 : Approximately well-balanced Discontinuous Galerkin methods using bases enriched with Physics-Informed Neural Networks

Orateur : Victor Michel-Dansac

This work concerns the enrichment of Discontinuous Galerkin (DG) bases, so that the resulting scheme provides a much better approximation of steady solutions to hyperbolic systems of balance laws. The basis enrichment leverages a prior – an approximation of the steady solution – which we propose to compute using a Physics-Informed Neural Network (PINN). To that end, after presenting the classical DG scheme, we show how to enrich its basis with a prior. Convergence results and error estimates show that the basis with prior does not change the order of convergence, and that the error constant is improved. To construct the prior, we elect to use parametric PINNs, which we introduce, as well as the algorithms to construct a prior from PINNs. We finally perform several validation experiments on four different hyperbolic balance laws to highlight the properties of the scheme. Namely, we show that the DG scheme with prior is much more accurate on steady solutions than the DG scheme without prior, while retaining the same approximation quality on unsteady solutions.

11h45 – 12h45 : Leveraging knowledge to design machine learning despite the lack of data using Transfer Learning and PINNS models

Orateur : Mathilde Mougeot

In recent years, considerable progress has been made in the implementation of decision support procedures based on machine learning methods through the exploitation of very large databases and the use of learning algorithms. In the industrial environment, the databases available in research and development or in production are rarely so voluminous and the question arises as to whether in this context it is reasonable to want to develop powerful tools based on artificial learning techniques. This talk presents research work around transfer learning and hybrid models that use knowledge from related application domains or physics to implement efficient models with an economy of data. Several achievements in industrial collaborations will be presented that successfully use these learning models to design machine learning for industrial small data regimes and to develop powerful decision support tools even in cases where the initial data volume is limited.

12h45 – 14h : Repas

14h – 14h45 : An incomplete overview of hybrid physics/machine learning modelling at Michelin – Focus on Physics Informed Neural Networks applications

Orateur : Thibault Dairay

Au cours de cette présentation, nous examinerons d’abord des cas concrets d’hybridation entre modèles physiques et modèles d’apprentissage permettant d’améliorer la précision et/ou de réduire les coûts de simulations effectuées dans le cadre de travaux de R&D chez Michelin. Nous nous pencherons ensuite sur l’application de la méthode Physics Informed Neural Networks (PINNs) à diverses explorations visant à estimer et/ou à identifier des quantités d’intérêt au sein d’un procédé de fabrication de la gomme constituant le pneumatique. Nous présenterons en particulier une méthode originale (Fixed Budget Online Adaptive Learning (FBOAL)) d’adaptation automatique des points de collocation utilisés dans l’apprentissage des réseaux PINNs.

14h45 – 15h15 : Geometry-aware framework for deep energy method: an application to structural mechanics with hyperelastic materials

Orateur : Khoa Nguyen

Physics-Informed Neural Networks (PINNs) have gained significant attention in various engineering fields thanks to their ability to incorporate physical laws into the models. Recently, geometry-aware models (GAPINNs) proposed to integrate geometric information into the model using the strong formulation of the physical systems underlying equations. However, the assessment of PINNs in problems involving different geometries remains an ongoing area of research. In this work, we introduce a novel physics-informed framework named the Geometry-Aware Deep Energy Method (GADEM) which uses a weak form of the physical system equations and aims to infer the solution on different shapes of geometries. We investigate different ways to represent the geometric information (using either spatial coordinates of the boundaries or images), and to encode the geometric latent vectors (such as explicit parametric encoding, linear dimensionality reduction (PCA), and non-linear algorithm (VAE)). The loss function minimizes the potential energy of all considered geometries. An adaptive learning method is employed for the sampling of unsupervised points to enhance the performance of GADEM. We present several applications of GADEM to solve solid mechanics problems involving hyperelastic materials. The numerical results of this work demonstrate the capability of GADEM to infer the solution on various shapes of geometries using only one trained model.

15h15 – 15h45 : pause

16h15 – 17h : PINNS for Projectile Motion

Orateur : Zaineb Chiha

In this work, we present a physic-Informed approach to model player-object scene in 3D dimension based on monocular vision. Using the parameterized system ODEs of the projectile motion and a small amount of simulated data we developed a PINNs model that predicts the 3D ball trajectories and to infer non-observed parameters.

• Human activity analysis and its interaction with the physical world using monocular computer vision (application to sport domain)
• Objective and Domain of interest
• Projectile Motion Case Study (Table Tennis) : Physical Study
• PINNS for Projectile Motion

Les organisateurs pour l’axe 4 de MIRES,

Guillaume Mercere guillaume.mercere@univ-poitiers.fr et Souad Bezzaoucha bezzaoucha@eigsi.fr