Manifold Learning with Implicit Physics Embedding for Reduced-Order Flowfield Modeling

Nonlinear manifold-learning (ML)-based reduced-order models (ROMs) can substantially improve the quality of nonlinear flowfield modeling. However, insufficient physical information often distorts the dimensionality-reduction process, reducing the robustness and accuracy of flowfield prediction. To address this problem, we propose a novel manifold-learning ROM with implicit physics embedding (IPE-ML). The approach involves initial dimensionality reduction followed by Gaussian process regression (GPR) to map physical parameters (e.g., angle of attack and Mach number) to manifold coordinates. These parameters are then iteratively incorporated into the manifold structure by minimizing GPR prediction error through online model updating, effectively fine-tuning the coordinates for a final, high-accuracy flowfield prediction model. Validated on transonic RAE2822 and supersonic hexagon airfoil cases, IPE-ML significantly improves the overall prediction accuracy of nonlinear flowfields. Specifically, errors near shock waves are notably reduced in the transonic case, while errors remain confined to small local regions in the supersonic case. This study offers a new perspective on embedding physical information into nonlinear ROMs.