A tool to improve the execution time of air quality models

Demіralp

2012

J Math Chem

This work aims to develop a new High Dimensional Model Representation (HDMR) based method which can construct an analytical structure for a given multivariate data modelling problem. Modelling multivariate data through a divideand-conquer method stands for multivariate data partitioning process in which we deal with a number of less variate data sets instead of a single N dimensional problem. Generalized HDMR is one of these methods used to model a multivariate data set which has a number of scattered nodes with associated function values. However, Generalized HDMR includes a linear equation system with huge number of unknowns and equations to be solved. This equation sometimes has linearly dependent equations in it and this is an undesirable situation. This work offers a new method named Piecewise Generalized HDMR method which bypasses this disadvantage as well as reducing the mathematical complexity and CPU time needed to complete the algorithm of the previous method. Our new method splits the given problem domain into subdomains, applies the Generalized HDMR philosophy to each subdomain and superpositions the information coming from these subdomains. The algorithm of this new method and a number of numerical implementations are given in this paper.

Section: Introductionmentioning

confidence: 99%

Multivariate data modelling through Piecewise generalized HDMR method

Demіralp

2012

J Math Chem

“…Sensitivity analysis for DSGE models using HDMR in economics and a state dependent parameter metamodelling with sensitivity analysis are developed by Ratto [14] and by Ratto, Pagano and Young [15] respectively. A tool to suppress the execution time of air quality models is developed by Gomez, Tchijov, Leon and Aguilar [16]. A neural network implementation based on RS-HDMR for potential energy surfaces is realized by Manzhos and Carrington [17].…”

Section: Introductionmentioning

confidence: 99%

Constancy maximization based weight optimization in high dimensional model representation

Demіralp

2009

Numer Algor

This work focuses on the weight function optimization in high dimensional model representation (HDMR) via constancy maximization. There are a lot of circumstances where HDMR's weight function becomes completely flexible in its factors. The univariate coordinate changes which can be constructed to produce nonnegative factors in the integrands of HDMR component, are perhaps the most important ones of these cases. Here, the weight function is considered as the square of a linear combination of certain basis functions spanning an appropriately chosen Hilbert space. Then, the coefficients of these linear combinations are determined to maximize the HDMR's constant term contribution to the function. Although the resulting equations are nonlinear we could have been able to approximate the solutions by using recently proven fluctuationlessness theorem on matrix representations appearing in the equations.

“…Many other scientists developed various HDMR-based methods for different research areas such as probabilistic analysis [15], reliability analysis [16], piece-wise continuous function approximation [17], modeling multiple input switching of CMOS gates [18], sensitivity analysis [19,20], decision making [21], black-box models [22,23], nonlinear models [24] and air quality models [25].…”

Section: Introductionmentioning

confidence: 99%

An approximation method to model multivariate interpolation problems: Indexing HDMR

Mathematical and Computer Modelling

2011

a b s t r a c tDealing with univariate or bivariate data sets instead of a multivariate data set is an important concern in interpolation problems and computer-based applications. This paper presents a new data partitioning method that partitions the given multivariate data set into univariate and bivariate data sets and constructs an approximate analytical structure that interpolates function values at arbitrarily distributed points of the given grid. A number of numerical implementations are also given to show the performance of this new method.