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

Abstract

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.

Theory-Guided Machine Learning in Materials Science

“…This could include groupings from dimensional analysis (Rajan et al, 2009), simple relational features (Kanter and Veeramachaneni, 2015), PCA (Sieg et al, 2006), or some other method. In all cases, care must be taken to avoid incompatible operations (e.g., do not add an atomic radius to an ionization potential).…”

What Is High-Throughput Virtual Screening? A Perspective from Organic Materials Discovery

“…Soft modeling is based on statistical learning methods to seek heuristic relationships between data (81) and it often uses developed descriptors as well as knowledge extracted through the previous tasks to construct a cheap yet robust model enabling the establishment and deeper understanding of QSAR/QSPR (65). It includes regressions, artificial neural networks, multivariate analysis, and other machine learning algorithms (85). Unlike hard modeling, the predictive soft modeling is particularly valuable when physical/chemical models are not available.…”

Perspective of Dimensional Analysis in Medical Science

“…position in space is described numerically by three scalars x, y and z, whereas a parameter in dimensional analysis is usually understood as a single quantity), which may in practice also lead to an unnecessary increase in the number of new parameters (Madrid & Alhama, 2006). These as well as other drawbacks of dimensional analysis are the reason why method is often aided by other dimensional reduction methods, with statistical methods among the most popular ones (Madrid & Alhama, 2006;Rajan et al, 2009). …”