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This paper focuses on the construction of accurate and predictive data-drivenreduced models of large-scale numerical simulations with complex dynamics andsparse training data sets. In these settings, standard, single-domainapproaches may be too inaccurate or may overfit and hence generalize poorly.Moreover, processing large-scale data sets typically requires significantmemory and computing resources which can render single-domain approachescomputationally prohibitive. To address these challenges, we introduce a domaindecomposition formulation into the construction of a data-driven reduced model.In doing so, the basis functions used in the reduced model approximation becomelocalized in space, which can increase the accuracy of the domain-decomposedapproximation of the complex dynamics. The decomposition furthermore reducesthe memory and computing requirements to process the underlying large-scaletraining data set. We demonstrate the effectiveness and scalability of ourapproach in a large-scale three-dimensional unsteady rotating detonation rocketengine simulation scenario with over $75$ million degrees of freedom and asparse training data set. Our results show that compared to the single-domainapproach, the domain-decomposed version reduces both the training andprediction errors for pressure by up to $13 \%$ and up to $5\%$ for other keyquantities, such as temperature, and fuel and oxidizer mass fractions. Lastly,our approach decreases the memory requirements for processing by almost afactor of four, which in turn reduces the computing requirements as well.

Improving the accuracy and scalability of large-scale physics-based data-driven reduced modeling via domain decomposition