Microsoft Teams Link: https://bit.ly/3nVqUhqModeling the behavior of complex heterogeneous materials requires both an adequate understanding of its internal spatial arrangement alongside local mechanical response. In recent decades hierarchical modeling techniques in which the microstructure is explicitly modeled, have provided new avenues for a greater understanding of the microstructure-dependent evolution of physical processes. Such explicit modeling of microstructural constituents enables a linkage between processes occurring in individual constituents and their effect on homogenized properties, providing valuable information for the design of materials. This work proposes research into establishing information flow in a bi-directional stochastic fashion across the coupled relationship between a materials' hierarchical internal structure, and its macro-scale effective property. The first task of this proposed research considers simultaneously solving a joint stochastic inverse problem across microstructure space and the space of meso-scale constitutive model parameters conditioned upon a sparse macro-scale experimental dataset. The resulting probabilistic understanding over these two domains could facilitate the production of increasingly robust microstructure-sensitive surrogate forward models through an improved understanding of local material behavior. This process represents a continuous linkage of information with macro-scale experimental data directly informing the behavior of the surrogate model. Subsequently, the second task will build from this constructed framework towards solving a high-dimensional stochastic inverse problem towards inverse microstructure design. The goal of this second research task is to determine conditional distributions of microstructures given a collection of target properties. Ideally, the framework established to tackle this problem will (i) be feasible over high-dimensional microstructure design spaces, enabling flexible designs, (ii) allow for multi-objective property design, and (iii) consist of a modular architecture such that previously established structure-property linkages can readily be incorporated. The collection of both tasks addresses several limitations within the field of Materials Informatics, and the results of which will further expand the capabilities of the computational material scientist in tailoring heterogeneous materials to meet targeted performance goals.