Ling-Ze Bu

Harbin University of Science and Technology · Department of Engineering Mechanics

To improve the computational efficiencies of the real-space orbital-free density functional theory, this work develops a new single-grid solver by directly providing the closed-form solution to the inner iteration and using an improved bisection method to accelerate the line search process in the outer iteration, and extended the single-grid solver...

The goals of this work are two-fold: firstly, to propose a new theoretical framework for representing random fields on a large class of multidimensional physical domain in the tensor train format; secondly, to develop a new algorithmic framework for accurately computing the modes and describing the correlation structure of the latent factors beyond...

The goals of this work are two-fold: firstly, to propose a new theoretical framework for representing random fields on a large class of multidimensional geometrical domain in the tensor train format; secondly, to develop a new algorithm framework for accurately computing the modes and the second and third-order cumulant tensors within moderate time...

To tackle the curse of dimensionality and multicollinearity problems of polynomial chaos expansion for analyzing global sensitivity and reliability of models with high stochastic dimensions, this paper proposes a novel non-intrusive algorithm called second order hierarchical partial least squares regression-polynomial chaos expansion. The first ste...

To meet the numerical challenges of polynomial chaos expansion for global sensitivity analysis in high stochastic dimensions, this paper proposes a new metamodeling method named hierarchical sparse partial least squares regression-polynomial chaos expansion (HSPLSR-PCE). Firstly, to avoid large data sets, the polynomials are divided into groups acc...

To circumvent the curse of dimensionality and multicollinearity problems of traditional polynomial chaos expansion approach when analyzing global sensitivity and structural reliability of high-dimensional models, this paper proposes a sparse partial least squares regression-polynomial chaos expansion metamodeling method. Firstly, an initial estimat...

To meet the numerical challenges of polynomial chaos expansion for global sensitivity analysis in high stochastic dimensions, this paper proposes a new metamodeling method named hierarchical sparse partial least squares regression-polynomial chaos expansion (HSPLSR-PCE). Firstly, to avoid large data sets, the polynomials are divided into groups acc...

To deal with the curse of dimensionality of polynomial chaos expansion for assessing reliability of structures with high stochastic dimensions, this paper proposes a novel non-intrusive algorithm based on a sparse partial least squares regression procedure. Firstly, an initial estimation of the expansion coefficients is obtained by performing parti...

To deal with the difficulty of polynomial chaos expansion in highdimensional problems, in this paper, we propose two algorithms that involve polynomial chaos expansion into partial least squares regression, which is a powerful tool in computational statistics. The performance of the hybrid algorithms was tested with two examples. Results illustrate...

Polynomial chaos expansion has been a mainstream method for global sensitivity and reliability analysis of structures due to its theoretical rigor, wide capability, convenient applicability and fast convergence in recent years. However, curse of dimensionality and multicollinearity have always been bottlenecks that prevent its application to large...