We present an accelerated greedy strategy for training of projection-based reduced-order models for parametric steady and unsteady partial differential equations. Our approach exploits hierarchical approximate proper orthogonal decomposition to speed up the construction of the empirical test space for least-square Petrov-Galerkin formulations, a progressive construction of the empirical quadrature rule based on a warm start of the non-negative least-square algorithm, and a two-fidelity sampling strategy to reduce the number of expensive greedy iterations. We illustrate the performance of our method for two test cases: a two-dimensional compressible inviscid flow past a LS89 blade at moderate Mach number, and a three-dimensional nonlinear mechanics problem to predict the long-time structural response of the standard section of a nuclear containment building under external loading.

翻译：本文提出一种加速贪婪策略，用于训练参数化定常与非定常偏微分方程的投影降阶模型。该策略通过以下技术加速模型构建：采用分层近似本征正交分解加速最小二乘Petrov-Galerkin公式中经验测试空间的构建；基于非负最小二乘算法的热启动渐进构建经验正交准则；以及采用双保真度采样策略减少高成本贪婪迭代次数。我们通过两个算例验证方法性能：中等马赫数下LS89叶片二维可压缩无粘绕流问题，以及考虑外部荷载下核安全壳标准段长期结构响应的三维非线性力学问题。