A parallel implementation of reduced-order modeling of large-scale systems
Ionut-Gabriel Farcas, Rayomand P. Gundevia, Ramakanth Munipalli, Karen E. Willcox
TL;DR
This paper tackles constructing physics-based reduced-order models for extremely large-scale aerospace simulations by introducing distributed Operator Inference (dOpInf). It combines POD-based dimensionality reduction with a fully discrete OpInf formulation in a parallel, MPI-enabled workflow, leveraging a step-by-step tutorial and a 2D Navier–Stokes cylinder benchmark to demonstrate implementation and scalability. The approach achieves a small ROM dimension (e.g., $r=10$) while preserving high fidelity (retained energy $\approx 99.96\%$) and provides practical guidelines for parallel data loading, transformations, dimensionality reduction, operator learning, and postprocessing. The results illustrate effective scalability and concrete procedures for integration into design, risk assessment, and uncertainty quantification tasks in complex aerospace applications, with open-source code available for practitioners.
Abstract
Motivated by the large-scale nature of modern aerospace engineering simulations, this paper presents a detailed description of distributed Operator Inference (dOpInf), a recently developed parallel algorithm designed to efficiently construct physics-based reduced-order models (ROMs) for problems with large state dimensions. One such example is the simulation of rotating detonation rocket engines, where snapshot data generated by high-fidelity large-eddy simulations have many millions of degrees of freedom. dOpInf enables, via distributed computing, the efficient processing of datasets with state dimensions that are too large to process on a single computer, and the learning of structured physics-based ROMs that approximate the dynamical systems underlying those datasets. All elements of dOpInf are scalable, leading to a fully parallelized reduced modeling approach that can scale to the thousands of processors available on leadership high-performance computing platforms. The resulting ROMs are computationally cheap, making them ideal for key engineering tasks such as design space exploration, risk assessment, and uncertainty quantification. To illustrate the practical application of dOpInf, we provide a step-by-step tutorial using a 2D Navier-Stokes flow over a step scenario as a case study. This tutorial guides users through the implementation process, making dOpInf accessible for integration into complex aerospace engineering simulations.