Multivariate active learning for polynomial chaos expansion (REC 2026 - 11th International Workshop on Reliable Engineering Computing: Reliability Computations in a Data and Model-Driven World, 2026)
The paper extends the active learning strategy of (Novák et al., 2021), which was originally designed for scalar-output polynomial chaos expansion surrogate models, to the case of vector-valued quantities of interest. Physical systems simulated by mathematical models typically contain multiple outputs (e.g., extrema in stress fields), and thus it is often necessary to construct several surrogate models for subsequent uncertainty quantification of each output. While the construction of surrogate models one-by-one for a single one-shot experimental design generated by various techniques (e.g., Latin Hypercube Sampling) is straightforward, an active learning methodology for multiple outputs remains an open research question. The proposed method combines the adaptivity of a polynomial chaos expansion with sequential sampling, enabling a one-by-one extension of the experimental design. The iterative process of sequential sampling selects points from a large pool of candidates by attempting to cover the design domain proportionally to their local variance contribution. The proposed criterion for sample selection balances between exploitation of the surrogate model and exploration of the design domain, while accounting for the different contributions of each output to the total criterion. The obtained numerical results confirm its superiority over standard non-sequential approaches in terms of surrogate model accuracy and estimation of output variance, especially with respect to extreme values.