Supervised machine learning of compressible flow past a rotating cylinder
High-fidelity numerical simulations of compressible flow past a rapidly rotating cylinder are used to investigate the evolution of aerodynamic loads and flow instability over a wide range of Reynolds numbers (Re = 1000 to 6000). The study reveals a transition from periodic vortex shedding to complex multi-mode oscillatory states, with a critical bifurcation identified near Re = 5650. Spectral analysis of lift and drag signals shows the emergence and interaction of multiple dominant frequencies, accompanied by amplitude modulation and nonlinear mode coupling in the post-bifurcation regime. To model these highly nonlinear dependencies, data-driven approaches are systematically explored using a database of 101 high-fidelity simulations (1 million core hours). Polynomial regression provides baseline fits but fails to capture localized fluctuations near bifurcation. Bayesian regression frameworks employing B-spline and Gaussian radial basis functions improve flexibility and uncertainty quantification, with spline-based models demonstrating superior performance in capturing piecewise nonlinear trends. Artificial neural networks (ANNs) are then developed as high-capacity surrogate models, achieving excellent predictive accuracy for maximum lift coefficient and instability onset time, while maintaining reasonable fidelity for the more challenging drag coefficient. Beyond regression, the ANN is further evaluated as a generative model to reconstruct flow behavior at unseen Re. A hierarchical refinement strategy is introduced, and results show that when trained on high-fidelity data, ANN-based models can serve as efficient and reliable surrogates for complex fluid dynamics problems.