SUMMARY

In the development of new/improved materials, it is essential to consider the evolutional path of the material structure. Prime examples of such material phenomena include grain growth, recrystallization, and phase transformation in polycrystals. Establishment of low-computational cost high-fidelity process-material structure (P-S) linkages are critical to dramatically accelerate the discovery and development of materials. This task is difficult due to the high dimensional description of the salient features within a material structure. Furthermore, the complexity is increased due to the multi-dimensional space of the processing parameters. Current approaches have largely considered relatively simple microstructures (e.g., two-phase microstructures) or highly simplified attributes of complex microstructures (e.g., grain size distribution) together with time series modeling to capture the P-S evolution linkages of interest. This thesis aims to demonstrate a versatile framework for systematic formulation of high-fidelity P-S evolution linkages across diverse materials phenomena via Gaussian process autoregression (GPAR) models while leveraging highly informative microstructure quantification. One of the central advantages of GPAR models is their ability to quantify the prediction uncertainty which provides invaluable guidance on the exploration of high dimensional input domain. The proposed framework encompasses four main steps: data generation via computationally intensive physics-based models, microstructure quantification, low dimensional representation of microstructures, and model building via GPAR. The versatility of the developed framework is shown through multiple case studies. It was seen that the framework developed in this study consistently produced remarkably accurate and robust, reduced-order, P-S evolution models for the diverse set of problems studied.