FastSVD-ML-ROM\textit{FastSVD-ML-ROM}: A Reduced-Order Modeling Framework based on Machine Learning for Real-Time Applications

Digital twins have emerged as a key technology for optimizing the performance of engineering products and systems. High-fidelity numerical simulations constitute the backbone of engineering design, providing an accurate insight into the performance of complex systems. However, large-scale, dynamic, non-linear models require significant computational resources and are prohibitive for real-time digital twin applications. To this end, reduced order models (ROMs) are employed, to approximate the high-fidelity solutions while accurately capturing the dominant aspects of the physical behavior. The present work proposes a new machine learning (ML) platform for the development of ROMs, to handle large-scale numerical problems dealing with transient nonlinear partial differential equations. Our framework, mentioned as $\textit{FastSVD-ML-ROM}$, utilizes $\textit{(i)}$ a singular value decomposition (SVD) update methodology, to compute a linear subspace of the multi-fidelity solutions during the simulation process, $\textit{(ii)}$ convolutional autoencoders for nonlinear dimensionality reduction, $\textit{(iii)}$ feed-forward neural networks to map the input parameters to the latent spaces, and $\textit{(iv)}$ long short-term memory networks to predict and forecast the dynamics of parametric solutions. The efficiency of the $\textit{FastSVD-ML-ROM}$ framework is demonstrated for a 2D linear convection-diffusion equation, the problem of fluid around a cylinder, and the 3D blood flow inside an arterial segment. The accuracy of the reconstructed results demonstrates the robustness and assesses the efficiency of the proposed approach.Comment: 35 pages, 22 figure

A voxelized immersed boundary (VIB) finite element method for accurate and efficient blood flow simulation

We present an efficient and accurate immersed boundary (IB) finite element (FE) method for internal flow problems with complex geometries (e.g., blood flow in the vascular system). In this study, we use a voxelized flow domain (discretized with hexahedral and tetrahedral elements) instead of a box domain, which is frequently used in IB methods. The proposed method utilizes the well-established incremental pressure correction scheme (IPCS) FE solver, and the boundary condition-enforced IB (BCE-IB) method to numerically solve the transient, incompressible Navier--Stokes flow equations. We verify the accuracy of our numerical method using the analytical solution for the Poiseuille flow in a cylinder, and the available experimental data (laser Doppler velocimetry) for the flow in a three-dimensional 90{\deg} angle tube bend. We further examine the accuracy and applicability of the proposed method by considering flow within complex geometries, such as blood flow in aneurysmal vessels and the aorta, flow configurations that would otherwise be difficult to solve by most IB methods. Our method offers high accuracy, as demonstrated by the verification examples, and high applicability, as demonstrated through the solution of blood flow within complex geometry. The proposed method is efficient, since it is as fast as the traditional finite element method used to solve the Navier--Stokes flow equations, with a small overhead (not more than 5$\%$) due to the numerical solution of a linear system formulated for the IB method.Comment: arXiv admin note: substantial text overlap with arXiv:2007.0208

Characterization, Reconstruction and Transport Properties of Vosges Sandstones Caractérisation, reconstruction et propriétés de transport des grès des Vosges

A thorough study of Vosges sandstone samples is presented in this work. First, the geometry of these porous media is analyzed using serial thin sections. Then, random numerical samples are reconstructed according to the measured statistical geometrical parameters. Finally, the macroscopic transport properties are determined from the numerical solutions in the reconstructed samples of the local equations governing the corresponding transport phenomena and compared to available experimental data. Mercury intrusion in the simulated media is modelled and pore size distribution results are compared with those obtained from serial tomography. Dans cet article, nous présentons une étude approfondie d'échantillons de grès des Vosges. La géométrie de ces milieux est analysée en utilisant des coupes sériées. Puis des échantillons aléatoires sont reconstruits en accord avec les propriétés géométriques statistiques mesurées. Enfin, les propriétés macroscopiques de transport sont déduites des solutions numériques dans les échantillons reconstruits des équations locales qui régissent les transports correspondants, et elles sont comparées aux mesures disponibles. La pénétration de mercure dans les échantillons est modélisée et les résultats relatifs aux distributions de pores sont comparés à ceux obtenus sur les coupes sériées

Characterization, Reconstruction and Transport Properties of Vosges Sandstones

International audienceA thorough study of Vosges sandstone samples is presented in this work. First, the geometry of these porous media is analyzed using serial thin sections. Then, random numerical samples are reconstructed according to the measured statistical geometrical parameters. Finally, the macroscopic transport properties are determined from the numerical solutions in the reconstructed samples of the local equations governing the corresponding transport phenomena and compared to available experimental data. Mercury intrusion in the simulated media is modelled and pore size distribution results are compared with those obtained from serial tomography

Characterization, Reconstruction and Transport Properties of Vosges Sandstones

A thorough study of Vosges sandstone samples is presented in this work. First, the geometry of these porous media is analyzed using serial thin sections. Then, random numerical samples are reconstructed according to the measured statistical geometrical parameters. Finally, the macroscopic transport properties are determined from the numerical solutions in the reconstructed samples of the local equations governing the corresponding transport phenomena and compared to available experimental data. Mercury intrusion in the simulated media is modelled and pore size distribution results are compared with those obtained from serial tomography