Active Learning–Based Surrogate Optimization Algorithm for Calibrating Computationally Expensive Geophysical Models

The reliability of computationally expensive geophysical and environmental models for simulating land surface processes strongly depends on accurate parameter calibration. However, traditional optimization algorithms often require thousands of model evaluations, making them unsuitable for such complex models. We propose an adaptive surrogate modeling-based optimization algorithm with active learning (ASMOAL), an efficient calibration framework that integrates surrogate modeling with a trust-region active learning strategy. At each iteration, ASMOAL adaptively selects informative parameter samples within a trust region, prioritizing high-potential and physically plausible regions, and updates the surrogate to guide the search toward improved solutions with limited model runs. 

We first evaluate ASMOAL on nine benchmark functions to verify convergence behavior and robustness. Then the algorithm is applied to three geophysical models with increasing complexity: the Variable Infiltration Capacity (VIC) model and the Xinanjiang (XAJ) model in two river basins in China, and the flash–Flood Event–based Spatially distributed rainfall–runoff Transformation (FeST) in two river basins in Italy. In addition, we conduct parameter sensitivity analysis to investigate how parameter relevance and interactions shape the search dynamics and accuracy of ASMOAL. The results demonstrate that sensitivity patterns can vary across basins and models, and that accounting for sensitivity information is critical for interpreting calibrated parameters and reducing the risk of equifinality. Moreover, the proposed algorithm exhibits improved convergence, calibration accuracy, and robustness compared to existing surrogate-based methods. The results also reveal that the optimal parameters obtained by ASMOAL tend to cluster within physically meaningful regions, highlighting the importance of focused search. The proposed ASMOAL algorithm offers a promising solution for enhancing parameter calibration in a wide range of computationally expensive geophysical and environmental models.