Effective combination of surrogate models and dimensionality reduction techniques for high-dimensional uncertainty quantification

The Monte Carlo (MC) method is most exact but computationally expensive for uncertainty quantification (UQ). Instead, surrogate models can approximate UQ at a lower computational cost. However, as the input uncertainty dimensionality increases, the number of samples required to construct the surrogate models also increases rapidly; thus, the advantage of using surrogate models disappears. Therefore, it is necessary to combine the surrogate models with dimensionality reduction for effective UQ. This study compares the performance of UQ for the direct MC method and four different combinations of surrogate models and dimensionality reduction methods in benchmark test functions. The results clarify the effectiveness of training a surrogate model and a dimensionality reduction technique simultaneously rather than separately.