Improved Sparse High-Dimensional Model Representation Based on Least Absolute Shrinkage and Selection Operator

Abstract

The increasing complexity of real-time problems has posed a perpetual challenge to existing simulation models. In particular, such models governing any physical system usually entail long hours of simulation, making them computationally intensive for large-scale problems. In order to mitigate this issue, a novel computational tool has been developed for efficient stochastic computations. The proposed model has been developed by two-tier improvement of the existing approximation techniques. As the first improvement, Kriging (Dubourg et al., in Probab Eng Mech 33: 47–57, 2013, [1]) has been incorporated within high-dimensional model representation (HDMR) (Li et al., in J Phys Chem A 110:2474–2485, 2006, [2]) model so as to enhance approximation capabilities in terms of accuracy. Second, least absolute shrinkage and selection operator (LASSO) (Tibshirani, in 1996, J. R. Stat. Soc. B 58:267–288, [3]) has been utilized and integrated with the refined model so as to construct a sparse HDMR approximation, eventually leading to reduced computational complexity. Implementation of the proposed approach has been demonstrated with two analytical benchmark examples and a 25-element space truss problem.