Adaptive PC-Kriging-Based sparse reduced-Order modeling framework for complex engineering systems

• A sparse HDMR framework is proposed, which builds components based on arbitrary Polynomial Chaos-Kriging(aPCK) and uses DIP to eliminate weak interaction terms, reduce computational costs, and maintain high accuracy. • Introduces Interaction-Focused Alternating Cut Sampling(IFACS) to balance global exploration and local feature capture in high-dimensional subspaces. • Validates on 30D nonlinear systems, achieving superior sample efficiency and robustness compared to KRG-HDMR, PCE-HDMR and PCK-HDMR. • The performance of the proposed method has been experimentally validated in different engineering examples including cantilever beams, composite beams, and Oldman River hydrological model. High-dimensional modeling of complex engineering systems often entails high computational costs and challenges in capturing nonlinear interactions. This study proposes an adaptive sparse reduced-order modeling framework based on Polynomial Chaos-Kriging(PC-Kriging). The framework integrates arbitrary Polynomial Chaos Expansion(PCE) with Kriging to deliver robust predictions under arbitrary input distributions. A Dynamic Interaction Pruning(DIP) mechanism is proposed to construct a sparse High-Dimensional Model Representation(HDMR), enabling decomposition and reduced-order modeling while significantly lowering computational costs. An adaptive sampling strategy further balances global exploration and local refinement, improving sampling efficiency in interaction subspaces. Validation on nonlinear benchmarks and engineering applications—including cantilever beams, composite structures, and hydrological systems—demonstrates up to 40% reduction in computational samples without compromising predictive accuracy or model robustness. The proposed framework offers an efficient and general tool for high-dimensional surrogate modeling and uncertainty quantification, providing practical support for data-driven design and performance assessment of complex engineering systems.