Classifier-based adaptive polynomial chaos expansion for high-dimensional uncertainty quantification

Abstract

A novel approach for the construction of polynomial chaos expansion (PCE) is proposed to facilitate high-dimensional uncertainty quantification (UQ). The current PCE techniques are well-known for UQ; however, they are affected by the curse of dimensionality that leads to over-fitting and tractability issues. Although L1-minimization can be used to deal with over-fitting, it is still ineffective for problems with a large number of independent random inputs or requiring a very high-order PCE. Therefore, a classifier-based PCE (CAPCE) is presented to mitigate the factorial growth of basis terms and prevent over-fitting. The adaptive framework includes four basis selection strategies – enrichment, screening, discovery, and recycling – in the inner loop and the enrichment of the training samples in the outer loop. Mainly, an adaptive classifier is trained on the dominant and discarded basis terms obtained from L1-minimization during discovery. It then allows the judicious selection of new higher-order basis candidates for L1-solver in the next iteration, thereby alleviating the effect of the curse of dimensionality. The proposed framework has been tested with analytical problems of varying sizes of independent random inputs and an engineering composite laminate problem. The comparison of CAPCE with the available efficient PCE techniques demonstrated improvements in accuracy using fewer samples due to a faster convergence rate.