Analyzing Sparse Data for Nitride Spinels Using Data Mining, Neural Networks, and Multiobjective Genetic Algorithms

Abstract

Nitride spinels are typically characterized by their unique AB₂N₄ structure containing a divalent cation A, a trivalent cation B, and an anion N. Numerous such species may exist as metals, semiconductors, or semimetals leading to their extensive usage in diverse scientific and engineering fields. Experimental and theoretical data on the physical or material properties of nitride spinels are, however, severely limited for coming up with a data driven, generic description for their material properties. In this study we have attempted to establish a methodology for handling such sparse data where the various features of some of the state of the art soft computing tools like Genetic Algorithms, Data Mining, and Neural Networks are used in tandem to construct some generic predictive models, in principle applicable to the nitride spinel structures at large, irrespective of their electronic characteristics. The paucity of the available data was circumvented in this work with a data mining strategy, important inputs were identified through an evolving neural net, and finally, the best possible tradeoffs between the bulk moduli and the relative stabilization energies of the nitride spinels were identified by constructing the Pareto-frontier for them through a Genetic Algorithms-based multiobjective optimization strategy.

Keywords:

• Data mining
• Evolutionary algorithm
• Genetic algorithms
• Multiobjective optimization
• Neural network
• Nitride spinels
• Spinels

ACKNOWLEDGMENTS

The authors (NC, CS, KR) gratefully acknowledge support from the National Science Foundation International Materials Institute program for Combinatorial Sciences and Materials Informatics Collaboratory (CoSMIC-IMI)–Grant No. DMR-0603644; AFOSR Grant No. FA95500610501 (KR) and the DARPA Center for Interfacial Engineering for MEMS (CIEMS)–Grant No. 1891874036790B (CS and KR). Travel and local hospitality support to one of the authors (NC) by Åbo Akademi University is also thankfully acknowledged. NC personally would like to thank Professor Bruce Harmon of Ames Laboratory USA, for inviting him to Ames in 2007 when a preliminary version of this study was initiated.

Notes

c.f. ☆Note that symbolic notations and expressions of crystal geometry for bond lengths and polyhedral volumes follows the work of Sickafus et al. [9]. Expressions of crystal geometry are based on the origin of structure at  m. In addition, ‘tet’ and ‘oct’ represent tetrahedral and octahedral cation sites, respectively, while ≤ and Δ represent an octahedral- and tetrahedral vacancy, respectively.

☆☆Derived parameters are combinations of descriptors or heuristic (i.e., physically intuitive) parameters.

¹Throughout this article, the complexity is expressed in terms of the number of weights in the lower part of the network. The bias terms are excluded. The number of parameters k however is determined by the total number of connections in both upper and lower parts of the network, including the biases.

²Although the network of complexity 8 indicates the lowest AIC value, it is rejected being unfavorable through both AICc and BIC criteria, and lack of its substantial difference from the AIC value obtained for the much smaller network of complexity 4.