Frédéric Magoulès

Shwetha Salimath, Francesca Bugiotti, Frederic Magoules

Metal forging is used to manufacture dies. We require the best set of input parameters for the process to be efficient. Currently, we predict the best parameters using the finite element method by generating simulations for the different initial conditions, which is a time-consuming process. In this paper, introduce a hybrid approach that helps in processing and generating new data simulations using a surrogate graph neural network model based on graph convolutions, having a cheaper time cost. We also introduce a hybrid approach that helps in processing and generating new data simulations using the model. Given a dataset representing meshes, our focus is on the conversion of the available information into a graph or point cloud structure. This new representation enables deep learning. The predicted result is similar, with a low error when compared to that produced using the finite element method. The new models have outperformed existing PointNet and simple graph neural network models when applied to produce the simulations.

Marien Chenaud, Frédéric Magoulès, José Alves

The recent rise of deep learning has led to numerous applications, including solving partial differential equations using Physics-Informed Neural Networks. This approach has proven highly effective in several academic cases. However, their lack of physical invariances, coupled with other significant weaknesses, such as an inability to handle complex geometries or their lack of generalization capabilities, make them unable to compete with classical numerical solvers in industrial settings. In this work, a limitation regarding the use of automatic differentiation in the context of physics-informed learning is highlighted. A hybrid approach combining physics-informed graph neural networks with numerical kernels from finite elements is introduced. After studying the theoretical properties of our model, we apply it to complex geometries, in two and three dimensions. Our choices are supported by an ablation study, and we evaluate the generalisation capacity of the proposed approach.

Marien Chenaud, José Alves, Frédéric Magoulès

Since the seminal work of [9] and their Physics-Informed neural networks (PINNs), many efforts have been conducted towards solving partial differential equations (PDEs) with Deep Learning models. However, some challenges remain, for instance the extension of such models to complex three-dimensional geometries, and a study on how such approaches could be combined to classical numerical solvers. In this work, we justify the use of graph neural networks for these problems, based on the similarity between these architectures and the meshes used in traditional numerical techniques for solving partial differential equations. After proving an issue with the Physics-Informed framework for complex geometries, during the computation of PDE residuals, an alternative procedure is proposed, by combining classical numerical solvers and the Physics-Informed framework. Finally, we propose an implementation of this approach, that we test on a three-dimensional problem on an irregular geometry.

Mengchen Wang, Nicolas Ferey, Patrick Bourdot et al.

This paper describes a work in progress about software and hardware architecture to steer and control an ongoing fluid simulation in a context of a serious game application. We propose to use the Lattice Boltzmann Method as the simulation approach considering that it can provide fully parallel algorithms to reach interactive time and because it is easier to change parameters while the simulation is in progress remaining physically relevant than more classical simulation approaches. We describe which parameters we can modify and how we solve technical issues of interactive steering and we finally show an application of our interactive fluid simulation approach of water dam phenomena.

Frederic Magoules, Qinmeng Zou

In this paper we present an original contactless human machine interface for driving car. The proposed framework is based on the image sent by a simple camera device, which is then processed by various computer vision algorithms. These algorithms allow the isolation of the user's hand on the camera frame and translate its movements into orders sent to the computer in a real time process. The optimization of the implemented algorithms on graphics processing unit leads to real time interaction between the user, the computer and the machine. The user can easily modify or create the interfaces displayed by the proposed framework to fit his personnel needs. A contactless driving car interface is here produced to illustrate the principle of our framework.