This paper focuses on the construction of accurate and predictive data-driven reduced models of large-scale numerical simulations with complex dynamics and sparse training datasets. In these settings, standard, single-domain approaches may be too inaccurate or may overfit and hence generalize poorly. Moreover, processing large-scale datasets typically requires significant memory and computing resources which can render single-domain approaches computationally prohibitive. To address these challenges, we introduce a domain decomposition formulation into the construction of a data-driven reduced model. In doing so, the basis functions used in the reduced model approximation become localized in space, which can increase the accuracy of the domain-decomposed approximation of the complex dynamics. The decomposition furthermore reduces the memory and computing requirements to process the underlying large-scale training dataset. We demonstrate the effectiveness and scalability of our approach in a large-scale three-dimensional unsteady rotating detonation rocket engine simulation scenario with over $75$ million degrees of freedom and a sparse training dataset. Our results show that compared to the single-domain approach, the domain-decomposed version reduces both the training and prediction errors for pressure by up to $13 \%$ and up to $5\%$ for other key quantities, such as temperature, and fuel and oxidizer mass fractions. Lastly, our approach decreases the memory requirements for processing by almost a factor of four, which in turn reduces the computing requirements as well.

翻译：本文聚焦于构建精确且具有预测能力的数据驱动降阶模型，用于处理具有复杂动力学特性和稀疏训练数据集的大规模数值模拟。在此类场景下，传统的单区域方法可能精度不足或容易过拟合，从而导致泛化能力较差。此外，处理大规模数据集通常需要大量的内存和计算资源，这可能使得单区域方法在计算上不可行。为应对这些挑战，我们在数据驱动降阶模型的构建中引入了区域分解框架。通过这种方式，降阶模型近似中所使用的基函数在空间上实现局部化，从而能够提高对复杂动力学进行区域分解近似的精度。该分解方法进一步降低了处理底层大规模训练数据集所需的内存和计算资源需求。我们通过一个具有超过7500万个自由度及稀疏训练数据集的大规模三维非定常旋转爆震火箭发动机模拟场景，验证了所提方法的有效性和可扩展性。结果表明，与单区域方法相比，区域分解版本将压力的训练误差和预测误差降低了高达13%，并将其他关键物理量（如温度、燃料与氧化剂质量分数）的误差降低了高达5%。最后，我们的方法将处理过程的内存需求降低了近四倍，从而也相应减少了计算需求。