<div>This dissertation addresses two significant issues in the effective application of machine learning algorithms and models for the physical and engineering sciences. The first is the broad challenge of automated modeling of data across different processes in a physical system. The second is the dilemma of obtaining insightful interpretations on the relationships between the inputs and outcome of a system as inferred from complex, black box machine learning models.</div><div><br></div><div><b>Automated Geometric Shape Deviation Modeling for Additive Manufacturing Systems</b></div><div><b><br></b></div><div>Additive manufacturing systems possess an intrinsic capability for one-of-a-kind manufacturing of a vast variety of shapes across a wide spectrum of processes. One major issue in AM systems is geometric accuracy control for the inevitable shape deviations that arise in AM processes. Current effective approaches for shape deviation control in AM involve the specification of statistical or machine learning deviation models for additively manufactured products. However, this task is challenging due to the constraints on the number of test shapes that can be manufactured in practice, and limitations on user efforts that can be devoted for learning deviation models across different shape classes and processes in an AM system. We develop an automated, Bayesian neural network methodology for comprehensive shape deviation modeling in an AM system. A fundamental innovation in this machine learning method is our new and connectable neural network structures that facilitate the transfer of prior knowledge and models on deviations across different shape classes and AM processes. Several case studies on in-plane and out-of-plane deviations, regular and free-form shapes, and different settings of lurking variables serve to validate the power and broad scope of our methodology, and its potential to advance high-quality manufacturing in an AM system.</div><div><br></div><div><b>Interpretable Machine Learning</b></div><div><b><br></b></div><div>Machine learning algorithms and models constitute the dominant set of predictive methods for a wide range of complex, real-world processes. However, interpreting what such methods effectively infer from data is difficult in general. This is because their typical black box natures possess a limited ability to directly yield insights on the underlying relationships between inputs and the outcome for a process. We develop methodologies based on new predictive comparison estimands that effectively enable one to ``mine’’ machine learning models, in the sense of (a) interpreting their inferred associations between inputs and/or functional forms of inputs with the outcome, (b) identifying the inputs that they effectively consider relevant, and (c) interpreting the inferred conditional and two-way associations of the inputs with the outcome. We establish Fisher consistent estimators, and their corresponding standard errors, for our new estimands under a condition on the inputs' distributions. The significance of our predictive comparison methodology is demonstrated with a wide range of simulation and case studies that involve Bayesian additive regression trees, neural networks, and support vector machines. Our extended study of interpretable machine learning for AM systems demonstrates how our method can contribute to smarter advanced manufacturing systems, especially as current machine learning methods for AM are lacking in their ability to yield meaningful engineering knowledge on AM processes. <br></div>