Multi-fidelity-based hierarchical scalable surrogate model for expanding design space

• A hierarchical scalable surrogate modeling (HSSM) framework is developed to enable efficient and accurate predictions in high-dimensional and dynamically expanding design spaces. • The framework integrates model filtering and multi-fidelity data fusion to construct extensible surrogates with enhanced robustness and reduced computational cost. • Validated on benchmark functions and engineering cases, HSSM demonstrates superior performance over conventional methods, offering a promising solution for real-time optimization and digital twin applications. With the growing complexity of engineering systems, traditional high-fidelity simulations increasingly fall short of meeting the real-time demands of structural optimization, control strategies, and digital twin applications. As a remedy, surrogate models have been introduced as cost-effective alternatives capable of approximating system behavior with substantially lower computational overhead. Nonetheless, their scalability remains limited, particularly in the face of high-dimensional design spaces or dynamic design requirements. To overcome these limitations, a hierarchical scalable surrogate modeling (HSSM) framework has been proposed, in which multi-fidelity strategies are employed to accommodate expanding design spaces without sacrificing predictive accuracy. Within the framework, two core modules (model filtering and data fusion) are introduced. Firstly, the base models are selected by evaluating four common surrogates (PRS, RBF, KRG, SVR) using root mean square error (RMSE) as the performance metric. Subsequently, a multi-fidelity scheme is applied to fuse low-fidelity models from the original design space with high-fidelity data from the expanded space, enabling the construction of a hierarchically extensible surrogate. The proposed approach is validated on fifteen benchmark functions and two engineering cases, through which enhanced accuracy and robustness are demonstrated compared to conventional methods. A scalable and adaptable modeling paradigm is thereby established for complex and evolving engineering systems.