Gaetan Raynaud

Bio: Gaetan Raynaud is an academic researcher from École Polytechnique de Montréal. The author has contributed to research in topics: Fourier transform & Degrees of freedom (mechanics). The author has co-authored 1 publications.

ModalPINN: an extension of Physics-Informed Neural Networks with enforced truncated Fourier decomposition for periodic flow reconstruction using a limited number of imperfect sensors

Abstract: Continuous reconstructions of periodic phenomena provide powerful tools to understand, predict and model natural situations and engineering problems. In line with the recent method called Physics-Informed Neural Networks (PINN) where a multi layer perceptron directly approximates any physical quantity as a symbolic function of time and space coordinates, we present an extension, namely ModalPINN, that encodes the approximation of a limited number of Fourier mode shapes. In addition to the added interpretability, this representation performs up to two orders of magnitude more precisely for a similar number of degrees of freedom and training time in some cases as illustrated through the test case of laminar shedding of vortices over a cylinder. This added simplicity proves to be robust in regards to flow reconstruction using only a limited number of sensors with asymmetric data that simulates an experimental configuration, even when a Gaussian noise or a random delay is added, imitating imperfect and sparse information.

Physics-Informed Neural Network (PINN) Evolution and Beyond: A Systematic Literature Review and Bibliometric Analysis

Abstract: This research aims to study and assess state-of-the-art physics-informed neural networks (PINNs) from different researchers’ perspectives. The PRISMA framework was used for a systematic literature review, and 120 research articles from the computational sciences and engineering domain were specifically classified through a well-defined keyword search in Scopus and Web of Science databases. Through bibliometric analyses, we have identified journal sources with the most publications, authors with high citations, and countries with many publications on PINNs. Some newly improved techniques developed to enhance PINN performance and reduce high training costs and slowness, among other limitations, have been highlighted. Different approaches have been introduced to overcome the limitations of PINNs. In this review, we categorized the newly proposed PINN methods into Extended PINNs, Hybrid PINNs, and Minimized Loss techniques. Various potential future research directions are outlined based on the limitations of the proposed solutions.

A stepwise physics‐informed neural network for solving large deformation problems of hypoelastic materials

Abstract: Physics-informed neural network (PINN) has been widely concerned for its higher computational accuracy compared with conventional neural network. The merit of PINN mainly comes from its ability to embed known physical laws or equations into data-based neural networks. However, when dealing with the rate-dependent nonlinear problems, such as elasto-plasticity with loading and unloading and hypoelastic large deformation, the conventional PINN cannot obtain satisfactory results. In this article, a stepwise physics-informed neural network (sPINN) is proposed to solve large deformation problems of hypoelastic materials. The whole process of sPINN can be divided into a series of time steps. In each time step, the rate constitutive equation expressed by Hughes-Winget algorithm and momentum governing equation are incorporated into the loss function as physical constraints. The displacement and stress fields can be resolved by completing the training process of each time step. Three numerical examples are designed to validate the proposed method by comparing with the solutions of FEM. The results show that sPINN can accurately resolve the displacement and stress fields in path-dependent large deformation problems. Furthermore, the performance of the sPINN on small data sets are also discussed, which illustrates that sPINN is more capable of predicting the global solution on small data sets as compared with conventional artificial neural network.