Block-structured Operator Inference for coupled multiphysics model reduction

TL;DR

This work introduces block-structured Operator Inference to learn reduced-order models (ROMs) for coupled multiphysics systems while preserving the intrinsic block form of each physics regime and their couplings. By assembling block-diagonal POD bases and learning separate operators for structural and fluid dynamics, the method reduces learning complexity, enables per-block regularization, and preserves stability and second-order structure. Applied to the AGARD 445.6 aeroelastic wing with FUN3D-generated data, the block-structured ROM achieves comparable accuracy to monolithic Operator Inference on training data and often better generalization for unseen initial conditions, while delivering an average online speedup of about 20%. The approach supports bilinear and quadratic couplings, allows intrusively specified blocks, and opens avenues for parametric extensions to flutter boundary characterization and beyond.

Abstract

This paper presents a block-structured formulation of Operator Inference as a way to learn structured reduced-order models for multiphysics systems. The approach specifies the governing equation structure for each physics component and the structure of the coupling terms. Once the multiphysics structure is specified, the reduced-order model is learned from snapshot data following the nonintrusive Operator Inference methodology. In addition to preserving physical system structure, which in turn permits preservation of system properties such as stability and second-order structure, the block-structured approach has the advantages of reducing the overall dimensionality of the learning problem and admitting tailored regularization for each physics component. The numerical advantages of the block-structured formulation over a monolithic Operator Inference formulation are demonstrated for aeroelastic analysis, which couples aerodynamic and structural models. For the benchmark test case of the AGARD 445.6 wing, block-structured Operator Inference provides an average 20% online prediction speedup over monolithic Operator Inference across subsonic and supersonic flow conditions in both the stable and fluttering parameter regimes while preserving the accuracy achieved with monolithic Operator Inference.

Figures (19)

• Figure 1: Structural mode shapes of the AGARD wing, scaled independently for visualization.
• Figure 2: Flutter boundaries from experiments yates1987agard and modeling silva2014agard in the literature (left) and training set flow conditions (right) for the AGARD 445.6 wing.
• Figure 3: Singular values for snapshot sets of size $k_\text{train} = 100$, $300$ and $500$. For each size, a different snapshot set is analyzed for each of the nine ($M_\infty$, $q_\infty$) flow conditions.
• Figure 4: Cumulative energy captured for varying $M_\infty$ and $q_\infty$ where $k_\text{train} = 300$ and thresholds are marked for at least 99.99% and 99.9995% cumulative energy captured.
• Figure 5: Centered and scaled nondimensional surface pressure portion of each POD mode for $M_\infty = 0.901$, $q_\infty = 50$ psf, and $k_\text{train} = 300$.