Component-Based Reduced Order Modeling of Large-Scale Complex Systems

Abstract

Large-scale engineering systems, such as propulsive engines, ship structures, and wind farms, feature complex, multi-scale interactions between multiple physical phenomena. Characterizing the operation and performance of such systems requires detailed computational models. Even with advances in modern computational capabilities, however, high-fidelity (e.g., large eddy) simulations of such a system remain out of reach. In this work, we develop a reduced‐order modeling framework to enable accurate predictions of large-scale systems. We target engineering systems which are difficult to simulate at a high-enough level of fidelity, but are decomposable into different components. These components can be modeled using a combination of strategies, such as reduced-order models (ROM) or reduced-fidelity full-order models (RF-FOM). Component-based training strategies are developed to construct ROMs for each individual component. These ROMs are then integrated to represent the full system. Notably, this approach only requires high-fidelity simulations of a much smaller computational domain. System-level responses are mimicked via external boundary forcing during training. Model reduction is accomplished using model-form preserving least-squares projections with variable transformation (MP-LSVT) (Huang et al., Journal of Computational Physics, 2022, 448: 110742). Predictive capabilities are greatly enhanced by developing adaptive bases which are locally linear in time. The trained ROMs are then coupled and integrated into the framework to model the full large-scale system. We apply the methodology to extremely complex flow physics involving combustion dynamics. With the use of the adaptive basis, the framework is demonstrated to accurately predict local pressure oscillations, time-averaged and RMS fields of target state variables, even with geometric changes.

Predictive Reduced Order Modeling of Chaotic Multi-scale Problems Using Adaptively Sampled Projections

“…Several remedies have been proposed to address this challenge through, for example, nonlinear bases [73,74,76,75], and online adaptation [83,80] etc. In the current work, the major focus is put on online adaption methods, which has been demonstrated by the current authors [86,87] necessary to construct truly predictive ROMs for chaotic fluid flow problems. An ideal adaption method would update the trial basis, V p , and the sampling points, S, during the online hyper-reduced ROM calculation (Eq.…”

“…One possible solution may be to collect a significant amount of FOM training data in the offline stage to construct the ROM, which, however, can eventually make the cost of ROM construction (offline training + online calculations) intractable and counters the purpose of ROM in general. On the other hand, the adaptive MOR discussed above opens a promising avenue to address this limitation by minimizing, or completely eliminating, the offline training stage requirement while building the ROM online, which inherently enhances the predictive capabilities of the ROM and enables true predictions of chaotic features in the problems [83,86,87].…”

A new method to interpolate POD reduced bases–Application to the parametric model order reduction of a gas bearings supported rotor

“…An established method addressing this task is the Interpolation on the Tangent Space to the Grassmann Manifold (ITSGM), recalled in Section 3, that has been successfully applied in a variety of situations. It is worth mentioning that other frameworks proceed differently by updating the reduced basis from new observed/computed snapshots 35‐37 …”

An adaptive, training‐free reduced‐order model for convection‐dominated problems based on hybrid snapshots

“…Adaptive reduced‐order models (AROMs) 22,25‐30 provide a different approach by continuously combining HDM and ROM operations. Predictive capabilities can be improved by alternating between HDM and ROM generated snapshots 25‐27 .…”