In computational mechanics, structural and process models are becoming increasingly complex in order to more accurately represent physical phenomena. This growing complexity leads to a significant increase in the number of input parameters and to higher computational costs for numerical simulations. To deal with this effects, machine-learning models (metamodels) are widely used to approximate the behavior of complex physical or numerical models at a reduced computational cost using measured or simulated data. Several metamodeling techniques have been proposed, including support vector machines (SVM), multilayer perceptrons (MLP), and Kriging. Among them, Kriging is commonly used due to its robustness, ease of implementation, interpolation capability, and inherent estimation of prediction uncertainty. Despite these advantages, classical Kriging techniques are generally limited to problems involving fewer than ten input parameters. To overcome this limitation, various approaches have been proposed, such as polynomial chaos expansion (PCE) kriging, principal component analysis (PCA) kriging, and high-dimensional model representation (HDMR) kriging. HDMR-based approaches are among the most promising, as they allow the treatment of models with hundreds of input parameters. However, the coupling of Kriging with HDMR remains under-exploited due to two major challenges: the difficulty of selecting an appropriate truncation order and the high computational cost associated with model training. The main objective of this work is to address both limitations. To this end, a reformulation of Kriging coupled with HDMR is proposed, in which the truncation order is determined adaptively. This A-HDMR Kriging approach automatically limits the consideration of high-order interactions when their influence is weak, thereby significantly reducing the number of required observations while maintaining an equivalent level of predictive accuracy.