Abstract We present an approach to build a reduced-order model for nonlinear, time-dependent, parametrized partial differential equations in a nonintrusive manner. The approach is based on combining proper orthogonal decomposition (POD) with a Smolyak hierarchical interpolation model for the POD coefficients. The sampling of the high-fidelity model to generate the snapshots is based on a locally adaptive sparse grid method. The novelty of the work is in the adaptive sampling of time, which is treated as an additional parameter. The goal is to have a robust and efficient sampling strategy that minimizes the risk of overlooking important dynamics of the system while disregarding snapshots at times when the dynamics are not contributing to the construction of the reduced model. The developed algorithm was tested on three numerical tests. The first was an advection problem parametrized with a five-dimensional space. The second was a lid-driven cavity test, and the last was a neutron diffusion problem in a subcritical nuclear reactor with 11 parameters. In all tests, the algorithm was able to detect and include more snapshots in important transient windows, which produced accurate and efficient representations of the high-fidelity models.

中文翻译：

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一种用于参数化时间相关问题的完全自适应非侵入式降阶建模方法

摘要 我们提出了一种以非侵入方式为非线性、时间相关、参数化偏微分方程构建降阶模型的方法。该方法基于将适当的正交分解 (POD) 与 POD 系数的 Smolyak 分层插值模型相结合。生成快照的高保真模型的采样基于局部自适应稀疏网格方法。这项工作的新颖之处在于时间的自适应采样，它被视为附加参数。目标是拥有一个强大而有效的采样策略，以最大限度地减少忽略系统重要动态的风险，同时在动态对简化模型的构建没有贡献时忽略快照。开发的算法在三个数值测试中进行了测试。第一个是用五维空间参数化的平流问题。第二个是盖子驱动的空腔测试，最后一个是亚临界核反应堆中的中子扩散问题，有 11 个参数。在所有测试中，该算法都能够在重要的瞬态窗口中检测并包含更多快照，从而为高保真模型提供准确有效的表示。