Abstract
Recent works have demonstrated the viability of convolutional neural networks (CNN) for capturing the highly non-linear microstructure-property linkages in high contrast composite material systems. In this work, we develop a new CNN architecture that utilizes a drastically reduced number of trainable parameters for building these linkages, compared to the benchmarks in current literature. This is accomplished by creating CNN architectures that completely avoid the use of fully connected layers, while using the 2-point spatial correlations of the microstructure as the input to the CNN. In addition to increased robustness (because of the much smaller number of trainable parameters), the CNN models developed in this work facilitate the construction of property closures at very low computational cost. This is because it allows for easy exploration of the space of valid 2-point spatial correlations, which is known to be a convex hull. Consequently, one can generate new sets of valid 2-point spatial correlations from previously available valid sets of 2-point spatial correlations, simply as convex combinations. This work demonstrates the significant benefits of utilizing 2-point spatial correlations as the input to the CNN, in place of the voxelated discrete microstructures used in current benchmarks.
Highlights
IntroductionThe microstructure of a material has a causal relationship with its effective anisotropic properties
(equivalent to pixels in 2-D and voxels in 3-D). Implicit in this representation is the assumption that there exist a finite number of distinct material local states, h 1, 2, . . . , H, which are allowed to occupy each spatial bin in the representative volume element (RVE), s 1, 2, . . . , S, to define the microstructure of interest
The Mean Absolute Error (MAE) loss function was utilized in this work for training the convolutional neural networks (CNN) model
Summary
The microstructure of a material has a causal relationship with its effective anisotropic properties. The microstructure-property relationships are most commonly explored using computationally expensive physics-based simulation tools (Ghosh et al, 1995; Kalidindi and Schoenfeld, 2000; Roters et al, 2010; Wargo et al, 2012; Brands et al, 2016) Such computational tools allow exploration mainly in the forward direction, i.e., going from given microstructures to the estimation of their effective properties. Of primary interest to this paper are the 2-point spatial correlations, which are captured in a discretized representation as an array denoted by fhrh’ The elements of this array reflect the probability of finding local states h and h′ in the RVE separated by a discretized vector indexed by an integer array r (very similar to s). 2-point spatial correlations are defined as (Kalidindi, 2015)
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