标题： 一种面向目标的自适应采样方法在具有超缩减的基于投影的约化阶模型中的应用 显示英文标题

标题： A Goal-Oriented Adaptive Sampling Procedure for Projection-Based Reduced-Order Models with Hyperreduction

摘要： 基于投影的降阶模型（PROMs）在许多应用中已经证明了其在近似高维、基于微分方程的计算模型方面的准确性、可靠性和鲁棒性。因此，它被提议作为一种工具用于高查询参数设计问题，比如现代飞机设计中出现的问题。由于空气动力学模拟可能计算成本高昂，PROMs 提供了对高保真解进行更快速估计的可能性。然而，效率仍然可能与全阶模型（FOM）的维度相关，特别是在由于非线性或参数依赖性导致需要频繁重新计算投影量时。对于 Petrov-Galerkin 模型，在每次 Newton 迭代中都会重新评估投影残差和 Jacobian，从而限制了预期的成本改进。超还原是可用于近似这些量并解决此问题的工具之一。本工作测试了能量守恒采样和加权（ECSW）方法作为超还原的一种潜在方法。它将被纳入到之前一篇文章 {10.1016/j.compfluid.2025.106568} 中的工作，该文章开发了一种自适应采样程序来构建具有受控函数误差的降阶模型（ROM）。通过 NACA0012 翼型研究超还原对计算成本和精度的影响。 显示英文摘要

摘要： Projection-based reduced-order models (PROMs) have demonstrated accuracy, reliability, and robustness in approximating high-dimensional, differential equation-based computational models across many applications. For this reason, it has been proposed as a tool for high-querying parametric design problems like those arising in modern aircraft design. Since aerodynamic simulations can be computationally expensive, PROMs offer the potential for more rapid estimations of high-fidelity solutions. However, the efficiency can still be tied to the dimension of the full-order model (FOM), particularly when projected quantities must be frequently recomputed due to non-linearities or parameter dependence. In the case of Petrov-Galerkin models, the projected residual and Jacobian are re-evaluated at every Newton iteration, thereby limiting the anticipated cost improvements. Hyperreduction is one of the tools available to approximate these quantities and address this issue. This work tests the energy-conserving sampling and weighting (ECSW) method as a potential approach for hyperreduction. It will be incorporated into the work in a previous article {10.1016/j.compfluid.2025.106568} which had developed an adaptive sampling procedure for building a reduced-order model (ROM) with a controlled functional error. The impacts of hyperreduction on computational cost and accuracy will be studied using the NACA0012 airfoil.