Heterogeneous materials are vital for both the modern engineer and inquisitive scientist alike. They make up a vital material class that can either form inevitably as a result of material processing (such as crystallization in metals) or can be intentionally designed for to gain desirable properties (such as anisotropy in composites). As such, due to their prevalence and applicability to various engineering problems, predicting their behavior has become a topic of great interest in the solid mechanics community over the last few decades.

One particularly pressing challenge is performing fast mechanical simulations along multiple length scales in heterogeneous materials. To this end, the reduced order method known as Self-Consistent Clustering Analysis (SCA) has been proposed as an effective means of striking a balance between accuracy and efficiency. Underpinning this is SCA's ability to decompose a domain into clusters in a preliminary offline stage (learning), efficiently reducing the problem's degrees of freedom. It has been shown to be remarkably accurate in predicting plasticity without significantly degrading accuracy compared to other methods, such as the finite element method. However, the offline stage requires a quantity known as the Cluster Interaction Tensor (CIT) to be computed, whose computational complexity scales quadratically with the number of clusters, thus causing a bottleneck in the method. Additionally, the CIT is recomputed during the online stage (prediction) in the recently proposed extension called adaptive Self-consistent Clustering Analysis (ASCA), which further stresses the need to speed up their computation.

To address this limitation, a data-driven surrogate model is proposed to compute the CIT efficiently. The behavior of the local CIT components is first analyzed, from which it is concluded that a surrogate model shall be developed to predict upper off-diagonal terms. This decision is made due to the bi-modal nature of certain components in the tensor and the quadratic scaling behavior of off-diagonal terms versus the linear scaling of diagonal ones. Following that, a sensitivity study shows how various magnitudes of noise affect the homogenized response's accuracy and convergence performance. Furthermore, it is shown that the solution accuracy and convergence behavior are degraded when the number of clusters is increased. With a proper understanding of the CIT's behavior and its function within SCA, the surrogate can be created.

The surrogate's feasibility is first shown using the ResNet-18 architecture, a CNN model derived from computer vision. It is demonstrated that ResNet-18 can make accurate predictions for a range of different microstructural parameters. This includes the number of clusters and samples in the dataset's distribution and out of distribution. Composite RVEs are used as out-of-distribution samples to test the robustness of the surrogate to realistic inputs. An attempt is made to improve the model's performance by training it on an unbalanced dataset, and although it improves the overall CIT prediction in specific regimes, the resulting stress-strain generalizability is degraded. Subsequently, a lighter version of ResNet-18, known as ResNet-lite, is tested and shown to give faster predictions than the baseline method. This, however, comes at a cost to the accuracy of the solution.

Additionally, deemed as a critical aspect of the study, the efficient generation of a large representative training dataset is discussed. A novel method for generating clustered microstructures efficiently using gradient noise is introduced. By leveraging datasets derived using this method, the surrogate can learn the fundamental interactions needed to make accurate predictions on realistic, out-of-distribution samples. The need for a large dataset is further emphasized using a dataset size sensitivity study.