Churn flow, a chaotic and oscillatory regime in vertical two-phase flow, has been lacking a quantitative mathematical definition for over 40 years. Researchers have now introduced a topology-based characterization using Euler Characteristic Surfaces (ECS), providing a breakthrough in understanding this complex phenomenon. By formulating unsupervised regime discovery as Multiple Kernel Learning (MKL), the study blends two complementary ECS-derived kernels, including temporal alignment, to improve the Wu flow-regime map in small-diameter vertical pipes. This approach enables a more accurate prediction of flow regimes, which is crucial in various industrial applications, such as oil and gas production, and chemical processing1. The significance of this study lies in its potential to enhance the design and operation of pipelines, thereby reducing the risk of accidents and improving overall efficiency, which matters to practitioners and engineers working in these fields.