SUMMARY

Over the last decade, the accessibility of expressive and large datasets has unlocked the transformative potential of data science and machine learning toolsets in a wide variety of fields. However, adoption of these toolsets in the sciences and engineering has been limited because of the challenge of curating such datasets. Materials Informatics – the study of materials behavior and processing using data science – is no exception. In this dissertation defense, I present a practical and theoretical analysis of the Stochastic Microstructure Function (SMF) formalism – a leading statistical formalism for the study of materials – that culminates in an overarching framework for the curation of large heterogeneous microstructure datasets. I touch on three topics relating to this goal: Microstructure Quantification, Statistically Conditioned Generation, and Dataset Curation. From the practical perspective, I will explore how each of these tasks can be efficiently and systematically addressed using elements of the SMF concept. In particular, I will present an exhaustive study of microstructure generation within this formalism. In addition to these practical developments, this dissertation defense grapples with two prominent theoretical questions. First, it analyzes the compatibility between the Stochastic Microstructure Function idea and modern deep learning techniques. I demonstrate the natural harmony that exists between the two, using deep learning models to estimate intractable elements of the SMF as well as using the SMF formalism to understand and direct the performance of deep learning models. Finally, I present a direct analysis of the SMF as a mathematical object, documenting the information content of its prominent statistical fingerprints, the n-point statistics. Teams Meeting ID: 220 028 385 937 Passcode: YaXjaL