Abstract:
In recent years, data-driven approaches have significantly reduced the computational
effort required to capture the structure-property linkages in high-contrast microstruc-
tures. Convolutional neural networks (CNNs), a special form of artificial neural
networks (ANNs), have been shown to produce high accuracy predictions of effective
properties of microstructures with greatly reduced computational effort in comparison
to traditional methods such as the Finite Element Method (FEM). This thesis investi-
gates the limits of the predictive abilities of CNNs for linear-elastic two-dimensional
high-contrast two-phase microstructures. The limits considered are different data
set sizes, contrast ratios, and sample sizes of two-dimensional microstructures. Fur-
thermore, the predictive accuracy of CNNs using data pre-processed with 2-point
spatial correlations in comparison to the original data is investigated. Additionally,
convolutional autoencoders and pre-trained models are compared against traditional
principal component analysis (PCA). For this purpose, several data sets containing
microstructures with a variety of sample sizes and contrast ratios were created. Select
elements of the linear-elastic stiffness tensor of a microstructure were computed using
FEM. CNNs were trained to predict these elements from the data sets to compare the
accuracies for different configurations. Furthermore, Autoencoders were trained on
spatial correlations and standard microstructures to investigate their reconstructive
abilities and determine which input format is best suited for reconstruction. Fully-
connected neural networks were trained using as inputs the outputs of Autoencoders
or principal component analysis (PCA) to compare the accuracy of both dimensionality
reduction methods. The results confirm the predictive power and efficiency of CNNs.
Also, the results suggest a slight decrease in predictive abilities for increasing contrast
ratios in microstructures. In contrast to previous works, no significant increase in
predictive accuracy can be generally detected when using 2-point correlations instead
of binary images as inputs to CNNs. Instead, a slight decrease in accuracy can be
observed in most cases. The results also suggest that the choice of filter sizes in CNNs
is very important in reducing the model size. Finally, from the comparison to other
models, it appears that accuracy can increase significantly in certain configurations
when pre-trained autoencoders are used for dimensionality reduction instead of PCA.