Efficient dimension reduction and surrogate-based sensitivity analysis for expensive models with high-dimensional outputs

摘要

Sensitivity analysis has been widely used to gain more insights on complex system behavior, to facilitate model reduction, system design and decision making. Typically, sensitivity analysis entails many evaluations of the system model. For expensive system models with high-dimensional outputs, direct adoption of such models for sensitivity analysis poses significant challenges in computational effort and memory requirements. To address these challenges, this paper proposes an efficient sensitivity analysis approach. The proposed method uses surrogate model to replace the expensive model for sensitivity analysis, and tackle the problem of building surrogate models for high-dimensional outputs through surrogate model integrated with dimension reduction. More specifically, the proposed method first uses surrogate models in low-dimensional latent output space to efficiently calculate the relevant covariance matrices for the low-dimensional latent outputs, and then directly establishes the sensitivity indices for the original high-dimensional output based on these covariance matrices and the derived transformation. Two examples are presented to demonstrate the efficiency and accuracy of the proposed method.