Numerical experiments on unsupervised manifold learning applied to mechanical modeling of materials and structures

Abstract

The present work aims at analyzing issues related to the data manifold dimensionality. The interest of the study is twofold: (i) first, when too many measurable variables are considered, manifold learning is expected to extract useless variables; (ii) second, and more important, the same technique, manifold learning, could be utilized for identifying the necessity of employing latent extra variables able to recover single-valued outputs. Both aspects are discussed in the modeling of materials and structural systems by using unsupervised manifold learning strategies.

Keywords

• Nonsupervised manifold learning
• State variables
• Dimensionality reduction
• $k$-PCA%22%2C%22default_operator%22%3A%22AND%22%7D%7D%7D"> <span class="mathjax-formula">$k$</span>-PCA
• Structural analysis
• Material constitutive equations