SUMMARY
Establishment of low-cost high-fidelity process-structure-property (P-S-P) linkages are critical to dramatically accelerate the discovery and development of advanced materials. This task is made challenging due to the inherently high dimensional, problem-specific features which describe the material structure. The recently developed Material Knowledge System (MKS) framework offers a data-driven framework for developing low-dimensional, information rich representations of the microstructures which are subsequently used to extract the P-S-P linkages of interest. However, the extraction of the reduced-order P-S-P linkages in not a trivial task. This is mainly attributed to (1) lack of a priori knowledge on the model form, (2) often small/sparse material datasets, (3) need for rigorous quantification of prediction uncertainties and (4) need for guiding experiments/simulations. These efforts are made even more challenging when considering P-S linkages. In the development of new/improved materials, it is essential and advantageous to consider the entire evolutional path of the material structure. The complexity is further increased due to the need for exploration of the often multi-dimensional processing space. In consideration of all the above; the naïve implementation of many surrogate modelling strategies is impractical. This thesis aims to establish a versatile Gaussian Process-MKS framework for systematic formulation of high-fidelity P-S-P linkages across diverse materials phenomena while leveraging highly informative microstructure quantification. The applicability of the GP-MKS framework is shown through multiple case studies. More specifically, the charge transport properties of organic photovoltaic polymers (S-P linkage) and microstructure evolution in polycrystalline materials undergoing static recrystallization and large-scale plastic deformation (P-S evolution linkages) are studied. In each case study, suitable extensions to MKS were made to best suit the specifications of the material problem at hand. The remarkably accurate robust P-S-P linkages established for the diverse set of studied problems attest to the versatility and tremendous potential of the developed GP-based MKS framework.