The increasing deployment of artificial intelligence (AI) models in high-stakes domains such as medical diagnostics and renewable energy has exposed persistent limitations in their generalizability and reproducibility across varying data sources and computational settings. AI models often fail to maintain stable performance when transferred to new environments, largely due to distributional shifts, limited annotated data, and differences in hardware or acquisition protocols. This thesis addresses the critical challenge of building generalizable AI systems and provides a structured framework for evaluating and fine-tuning these models across diverse domains.

The core contribution of this dissertation is the development and analysis of foundational models that can be pretrained on heterogeneous datasets and subsequently adapted to new target domains using minimal site-specific data. These models are evaluated in two applied contexts: prostate cancer detection using MRI radiomics, and solar cell performance prediction using simulated photovoltaic datasets. In both domains, the research demonstrates that transfer learning, combined with carefully designed harmonization pipelines and explainability modules, leads to substantial improvements in cross-site adaptability and clinical or scientific relevance.

The theoretical component of the work explores the mathematical principles underlying generalizable learning. Drawing on concepts from Poisson’s equations, continuity equations, and Lyapunov stability, the study proposes an exponential decay mechanism as a theoretically sound learning rate schedule for future implementation. This framework introduces the notion of equiconnectedness ensuring that the superlevel sets of the loss function remain connected under dynamic regularization thereby offering a foundation for convergence stability in overparameterized models. Although not applied in the practical domains presented, these mathematical insights provide direction for the principled design of future optimization strategies.

In the photovoltaic application, a Bayesian Regularized Neural Network is trained on over a million simulated configurations of silicon tandem multi-junction solar cells. The model accurately predicts performance metrics such as open-circuit voltage and fill factor, enabling data-driven optimization of solar devices under diverse environmental conditions. In the medical imaging application, a Vision Transformerbased model is pretrained on radiomic features extracted from multiparametric prostate MRI scans and fine-tuned on site-specific datasets. The model achieves an average AUC of 0.85, with improved results upon local adaptation, and demonstrates robust performance across different scanner vendors and imaging protocols. Integration of SHAP and LIME further facilitates clinical interpretability.

In conclusion, this dissertation contributes to the development of generalizable AI systems by combining practical model-building strategies with rigorous mathematical theory. This dissertation advances the field of artificial intelligence by developing mathematically grounded optimization strategies that enhance neural network performance and stability. By successfully applying these strategies to complex, high-dimensional data landscapes in photovoltaics and medical diagnostics, the research demonstrates the broad applicability and impact of integrating rigorous mathematical theory with practical neural network design and optimization.