Hierarchical multi-fidelity surrogate modeling with curvature- and uncertainty-driven sampling for fluid flow prediction

In computational fluid dynamics and related applications, surrogate modeling often faces a fundamental trade-off between data acquisition cost and model accuracy. Multi-fidelity surrogate modeling and adaptive sampling have emerged as effective strategies to address this challenge: the former integrates limited high-fidelity data with abundant low-fidelity data, while the latter enhances efficiency through informed sampling criteria. This work presents a novel framework, hierarchical multi-fidelity surrogate modeling with adaptive sampling (HMFS-AS), designed to improve data efficiency in fluid flow modeling tasks. The method consists of two main components. First, the hierarchical multi-fidelity surrogate (HMFS) decomposes fidelity discrepancies into linear and nonlinear components, with the nonlinear residual modeled via Gaussian process regression, which naturally provides predictive uncertainty to guide sampling. Second, the adaptive sampling scheme includes two strategies: curvature-guided sampling, which leverages curvature information extracted from a neural network surrogate trained on low-fidelity data to select informative initial high-fidelity samples; and uncertainty-driven sampling, which iteratively refines the surrogate based on predictive uncertainty. The proposed HMFS-AS framework is validated on two benchmark problems and further demonstrated on three fluid dynamics cases: lift-to-drag ratio prediction for a National Advisory Committee for Aeronautics 0012 (NACA 0012) airfoil, structural response under dam-break flow, and surrogate modeling of a fluidized bed process dataset. Results show that HMFS-AS outperforms several multi-fidelity methods in both accuracy and robustness, demonstrating its potential for data-efficient modeling in complex fluid flow scenarios.