Principal component analysis and dimensional analysis as materials informatics tools to reduce dimensionality in materials science and engineering

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Abstract

In engineering design, we are constantly faced with the need to describe the behavior of complex engineered systems for which there is no closed-form solution. There is rarely a single multiscale theory or experiment that can meaningfully and accurately capture such information primarily due to the inherently multivariate nature of the variables influencing materials behavior. Seeking structure-property relationships is an accepted paradigm in materials science, yet these relationships are often not linear, and so the challenge is to seek patterns among multiple length and time scales. In this paper, we present two separate but complementary examples of addressing the issue of high-dimensional data in materials science in the spirit of the intellectual focus of this new journal. The first example uses principal component analysis and the second example uses statistical analysis coupled to dimensional analysis. Copyright © 2009 Wiley Periodicals, Inc., A Wiley Company

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