Extrapolative prediction in multiphase flow pipelines: a multi-fidelity surrogate approach with stacking ensemble

Accurate extrapolation of multiphase flow behaviour in offshore pipelines is hindered by limited field data, simulator bias, and strong nonlinearities. A multi-fidelity surrogate approach with stacking ensemble is proposed to address these challenges, in which a field-trained high-fidelity expert and a simulation-trained expert are adaptively fused through a k-nearest-neighbours (k-NN) competence metric and a Lipschitz-continuous convex combiner. This design ensures mean-squared-error dominance, such that the fused predictor never underperforms the better expert and variance is suppressed in transitional regimes. Data efficiency is further enhanced by a hybrid active learning strategy (ZECR Sampling) that integrates geometric coverage with uncertainty-driven refinement. When applied to a real offshore pipeline dataset containing more than 5,700 samples, the proposed method achieves an R2 of 0.740 and reduces RMSE by over 20% compared with the best baseline. These results indicate that the framework functions not only as a fast surrogate but also as a spatially aware risk controller, enabling reliable extrapolative prediction and supporting automated, real-time decision-making in multiphase flow pipeline systems.