An efficient algorithm to accelerate the discovery of complex material formulations

Abstract

The identification of complex multicomponent material formulations that possess specific optimal properties is a challenging task in materials discovery. The high dimensional composition space needs to be adequately sampled and the properties measured with the goal of efficiently identifying effective formulations. This task must also take into account mass fraction and possibly other constraints placed on the material components. Either combinatorial or noncombinatorial sampling of the composition space may be employed in practice. This paper introduces random sampling-high dimensional model representation (RS-HDMR) as an algorithmic tool to facilitate these nonlinear multivariate problems. RS-HDMR serves as a means to accurately interpolate over sampled materials, and simulations of the technique show that it can be very efficient. A variety of simulations is carried out modeling multicomponent-->property relationships, and the results show that the number of sampled materials to attain a given level of accuracy for a predicted property does not significantly depend on the number of components in the formulation. Although RS-HDMR best operates in the laboratory by guided iterative rounds of random sampling of the composition space along with property observation, the technique was tested successfully on two existing databases of a seven component phosphor material and a four component deNO(x) catalyst for reduction of NO with C(3)H(6).

Variable Selection in Regression Models Using Global Sensitivity Analysis

“…These measures are based on the standard variance decomposition formula, or 'law of total variance' (Billingsley 1995), Problem 34.10(b)). In the context of GSA, these decomposition formulae are discussed in Archer, Saltelli, and Sobol (1997), Saltelli and Tarantola (2002), Sobol' (1993), Brell, Li, and Rabitz (2010). For further reading about GSA in their original setting, see Saltelli et al (2012).…”

Exploring Hoover and Perez's experimental designs using global sensitivity analysis

“…Billingsley (1995), Problem 34.10(b). In the context of GSA these decomposition formulae are discussed in Archer et al (1997), Saltelli and Tarantola (2002), Sobol' (1993), Brell et al (2010). For further reading about GSA in their original setting, we refer to Saltelli et al (2012).…”

First- and Second-Order Local and Global Sensitivity Analyses on Ignition Delay Times of Four Typical Fuels

“…Several methods have been developed to perform global sensitivity analysis 8,10,11,16,[26][27][28]31,32 Global sensitivity analysis through an optimized high-dimensional model representation method using a random sampling of inputs(RS-HDMR) has been implemented in the GUI_HDMR program by Ziehn and Tomlin 10,26,[29][30][31][32][33][34][35] . A relatively small number of samples is needed to carry out global sensitivity analysis using the GUI_HDMR program and it is presently one of the most popular global sensitivity analysis method in analysis of combustion models 26,29,30,33,34,[36][37][38][39][40][41][42][43][44][45][46] . Recently, the artificial neural network method 28 has been adopted to further reduce computational effort in HDMR method.…”

“…In a chemical kinetic model for combustion process, there usually exist several hundreds or even thousands of input parameters and the most important 20-30 input parameters are chosen based on physical consideration or firstorder local sensitivity coefficients. Third-order or even higherorder sensitivity coefficients can be determined in principle with HDMR, however, only first and second-order global sensitivity coefficients are calculated in practice 26,29,30,33,34,[36][37][38][39][40][41][42][43][44][45][46] .…”