Multivariate Active Learning for Engineering Uncertainty Quantification

In complex engineering applications, high-fidelity models often produce multiple quantities of interest (QoIs) from the same input parameters, such as in finite element simulations. Directly evaluating these models is computationally expensive, leading to the widespread use of surrogate models for efficient approximation. However, a single experimental design (ED) may not adequately represent all outputs simultaneously, especially when different QoIs have varying sensitivities to input variables. To address this, researchers have generalized an adaptive sequential sampling method for constructing polynomial chaos expansion (PCE) surrogate models to accommodate vector-valued QoIs. This approach avoids the increased sampling complexity and data inconsistency of separate sampling for each output. The proposed method sequentially selects new samples from a candidate pool, prioritizing those that locally contribute most to output variance. It intelligently balances exploration of the input space with exploitation of aggregated variance information across all outputs. Numerical examples from engineering problems demonstrate that this strategy significantly enhances both the accuracy and stability of the surrogate models, providing more reliable estimations of second-order statistics compared to non-sequential Latin Hypercube Sampling.