Adaboost-based ensemble of polynomial chaos expansion with adaptive sampling

In the study, we propose a new polynomial chaos expansion surrogate modeling method based on Adaboost (Adaboost-PCE) for uncertainty quantification. Adaboost is an ensemble learning technique originating from the machine learning field. The idea of Adaboost-PCE is to construct many times the “weak” PCE model with assigned weights to each sample point. Each time, the weight of a particular sample point in the training set depends on the performance of the surrogate models on that sample. In this way, weighted least-squares approximation is employed to exploit the weights of each sample in order to reduce the effect of outliers. The Adaboost-PCE is appealing since it is possible to estimate the ensemble weights without using any explicit error metrics as in most existent ensemble methods. Moreover, it has an expectation of the prediction error that enables the efficient adaptive sampling. The proposed method is validated with a numerical comparison of their performance on a series of numerical tests including partial differential equations with high-dimensional inputs.