Understanding and visualizing microstructure and microstructure variance as a stochastic process

Context Aware Machine Learning Approaches for Modeling Elastic Localization in Three-Dimensional Composite Microstructures

“…In other words, m h s takes values of 0 or 1 depending on the local state occupying each voxel in each MVE. Similar descriptions have been successfully implemented in prior work for microstructure classification [9,10,25], microstructure reconstructions [47], and establishing process-structure-property linkages [28,30,34,44].…”

“…All three multiagent systems proposed in this paper achieve a test MASE around 8%, which validates that the concept of context extraction is constructive in producing more accurate prediction systems. It should be noted that the error measures of "M3" can be further reduced by using more rigorous microstructure quantification methods [9,25,28,30]. It is also rather trivial to impose a multi-agent layer onto any existing prediction system.…”

“…4 Individual MASE attained by the three proposed context detection systems for each of the 1000 MVEs in test set, along with the MASE for the best single agent system [7] (Color figure online) the dimensions of the microstructure representation. In our prior work, PCA was successfully implemented for both dimensionality reduction [23,25], microstructure classification [9,10], process-structure-property linkages [28,30]. PCA performs the dimensionality reduction by transforming the coordinate system where the data is represented in such a way that the components of the new coordinate system are ordered from highest variance to lowest variance.…”

Process-Structure Linkages Using a Data Science Approach: Application to Simulated Additive Manufacturing Data

“…Although a number of options exist for dimensionality reduction, PCA was chosen here because it offers the following benefits: (i) it is a distance-preserving transformation, which allows a highly accurate and low-cost computation of a difference measure between any two microstructures using just the low-dimensional representations, (ii) it provides an orthogonal basis for representing the microstructure statistics which should lead to robust representations of process-structure-property (PSP) linkages, (iii) easy access to highly efficient computational toolsets for computing PCA on large datasets [67,71,72], (iv) a remarkable ability to recover the original high-dimensional microstructure statistics with only a handful of PC scores as long as the eigenvectors found in the PCA are stored [47], and (v) prior success in establishing robust PSP linkages in a wide range of multiscale materials phenomena [47,73,74]. Consequently, for each microstructure indexed by m, its feature vector (set of three chord length distributions representing a total of 503 chord length statistics) denoted by CLD m can be approximately decomposed into a linear combination of basis vectors (called principal components) and weights (i.e., PC scores) [74] such that…”

Novel microstructure quantification framework for databasing, visualization, and analysis of microstructure data

“…Ganapathysubramanian and Zabaras explored more advanced non-linear dimensionality reduction schemes and used these representations to construct inputs to stochastic multi-scale models [9,10]. Niezgoda [11] and Niezgoda, Yabansu and Kalidindi [12] formalized the description of microstructure via statistical metrics into a stochastic process interpretation, and developed the basic theory for the microstructure visualization space presented in this work. Additionally, they developed relationships between the observed variance in microstructure for a material ensemble and the corresponding ensemble variance in properties/performance and proposed applications of the microstructure visualization space in materials design and manufacturing quality control and process monitoring.…”