  High-performance computing (HPC) has revolutionized our ability to perform
detailed simulations of complex real-world processes. A prominent contemporary
example is from aerospace propulsion, where HPC is used for rotating detonation
rocket engine (RDRE) simulations in support of the design of next-generation
rocket engines; however, these simulations take millions of core hours even on
powerful supercomputers, which makes them impractical for engineering tasks
like design exploration and risk assessment. Reduced-order models (ROMs)
address this limitation by constructing computationally cheap yet sufficiently
accurate approximations that serve as surrogates for the high-fidelity model.
This paper contributes a new distributed algorithm that achieves fast and
scalable construction of predictive physics-based ROMs trained from sparse
datasets of extremely large state dimension. The algorithm learns structured
physics-based ROMs that approximate the dynamical systems underlying those
datasets. This enables model reduction for problems at a scale and complexity
that exceeds the capabilities of existing approaches. We demonstrate our
algorithm's scalability using up to $2,048$ cores on the Frontera supercomputer
at the Texas Advanced Computing Center. We focus on a real-world
three-dimensional RDRE for which one millisecond of simulated physical time
requires one million core hours on a supercomputer. Using a training dataset of
$2,536$ snapshots each of state dimension $76$ million, our distributed
algorithm enables the construction of a predictive data-driven reduced model in
just $13$ seconds on $2,048$ cores on Frontera.
