🤖 AI Summary
This study addresses the challenges of insufficient surrogate accuracy and low sampling efficiency in high-fidelity engineering models with multi-output responses, where conventional single-output modeling neglects inter-output correlations and incurs high computational costs. To overcome these limitations, this work proposes a multivariate active learning strategy based on polynomial chaos expansion for vector-valued outputs. The approach introduces a sequential sampling criterion that jointly exploits statistical correlations among outputs and balances exploration of the input space with exploitation of joint output variance information. By preserving data consistency across outputs, the method significantly enhances both sampling efficiency and global model accuracy. Numerical experiments on multiple engineering benchmarks demonstrate its superior performance in surrogate fidelity, numerical stability, and uncertainty quantification of second-order statistics.
📝 Abstract
In many engineering applications, a single high-fidelity model produces multiple quantities of interest (QoIs) under the same input parameters, e.g. finite element models of complex physical systems. To alleviate the high computational cost of direct model evaluations, surrogate models are widely used to construct efficient approximations of model responses. Naturally, the accuracy of surrogates strongly depends on the quality of the experimental design (ED). However, a single ED may not provide an adequate representation for all outputs simultaneously, especially when different outputs exhibit varying sensitivities to the input variables. A straightforward solution is to perform separate sampling for each output, but this results in increased sampling complexity and computational cost. From a statistical perspective, such an approach also ignores potential correlations among all outputs and may compromise data consistency. To address this issue, an adaptive sequential sampling method for constructing polynomial chaos expansion surrogate models is generalized for vector valued QoIs. The method sequentially selects new samples from a candidate pool based on their local contribution to the output variance, while balancing distance-based exploration of the input space and exploitation of aggregated variance information across all outputs. Its performance is compared with non-sequential Latin Hypercube Sampling through several numerical examples from engineering problems. Numerical results demonstrate that the proposed strategy improves both surrogate accuracy and stability, and provides a more reliable estimation of second-order statistics.