A hybrid numerical methodology coupling Reduced Order Modeling and Graph Neural Networks for non-parametric geometries: applications to structural dynamics problems
Université Paris-Saclay（巴黎萨克雷大学）；CentraleSupélec（中央理工-高等电力学院）；ENS Paris-Saclay（巴黎萨克雷高等师范学校）；CNRS（法国国家科学研究中心）；LMPS - Laboratoire de Mécanique Paris-Saclay（巴黎萨克雷力学实验室）；Safran Tech（赛峰技术公司）
Victor Matray, Faisal Amlani, Frédéric Feyel, David Néron
This work introduces a new approach for accelerating the numerical analysis of time-domain partial differential equations (PDEs) governing complex physical systems. The methodology is based on a combination of a classical reduced-order modeling (ROM) framework and recently-introduced Graph Neural Networks (GNNs), where the latter is trained on highly heterogeneous databases of varying numerical discretization sizes. The proposed techniques are shown to be particularly suitable for non-parametric geometries, ultimately enabling the treatment of a diverse range of geometries and topologies. Performance studies are presented in an application context related to the design of aircraft seats and their corresponding mechanical responses to shocks, where the main motivation is to reduce the computational burden and enable the rapid design iteration for such problems that entail non-parametric geometries. The methods proposed here are straightforwardly applicable to other scientific or engineering problems requiring a large number of finite element-based numerical simulations, with the potential to significantly enhance efficiency while maintaining reasonable accuracy.
Neural Network-Based Parametric Model Reduction for Predicting Turbulent Flow for Different Vehicle Geometries
Operations and Computer Technologies Division, RIKEN Center for Computational Science（RIKEN中心计算科学研究所运算与计算机技术部门）；Complex Phenomena Unified Simulation Research Team, RIKEN Center for Computational Science（RIKEN中心计算科学研究所复杂现象统一模拟研究团队）；Department of Computational Science, Graduate School of System Informatics, Kobe University（神户大学系统信息学研究院计算科学系）
A Physics-Informed Meta-Learning Framework for the Continuous Solution of Parametric PDEs on Arbitrary Geometries
Graduate School of Science and Technology, Keio University（Keio大学科学技术研究生院）；Department of Mechanical Engineering, Keio University（Keio大学机械工程系）；Access e.V.
CGAN-EB: A Non-parametric Empirical Bayes Method for Crash Hotspot Identification Using Conditional Generative Adversarial Networks: A Real-world Crash Data Study
