Understanding The Effects of Incorporating Scientific Knowledge on Neural Network Outputs and Loss Landscapes

While machine learning (ML) methods have achieved considerable success on several mainstream problems in vision and language modeling, they are still challenged by their lack of interpretable decision-making that is consistent with scientific knowledge, limiting their applicability for scientific discovery applications. Recently, a new field of machine learning that infuses domain knowledge into data-driven ML approaches, termed Knowledge-Guided Machine Learning (KGML), has gained traction to address the challenges of traditional ML. Nonetheless, the inner workings of KGML models and algorithms are still not fully understood, and a better comprehension of its advantages and pitfalls over a suite of scientific applications is yet to be realized. In this thesis, I first tackle the task of understanding the role KGML plays at shaping the outputs of a neural network, including its latent space, and how such influence could be harnessed to achieve desirable properties, including robustness, generalizability beyond training data, and capturing knowledge priors that are of importance to experts. Second, I use and further develop loss landscape visualization tools to better understand ML model optimization at the network parameter level. Such an understanding has proven to be effective at evaluating and diagnosing different model architectures and loss functions in the field of KGML, with potential applications to a broad class of ML problems.