Abstract

Accurate modeling of complex systems is crucial in domains such as healthcare, where personalized diagnosis and treatment planning are essential. Traditional physics-based models provide structured, theoretically grounded insights but are often computationally intensive and constrained by simplified assumptions that limit adaptability to patient-specific conditions. In contrast, data-driven models are computationally efficient and capable of capturing complex patterns, yet they often lack interpretability and fail to incorporate essential physical principles, reducing robustness and generalization. This disconnect between mechanistic understanding and computational practicality presents significant challenges in critical applications such as healthcare, where both physical accuracy and real-time performance are vital. To address these challenges, this dissertation presents hybrid modeling frameworks that integrate the predictive power of data-driven approaches with the theoretical rigor of physics-based modeling, aiming to develop accurate and interpretable models for real-time applications in complex systems. It advances these goals through two primary research directions: (1) residual modeling, which bridges gaps between physics-based predictions and empirical data, and (2) physics-guided learning, which embeds physical laws within neural network training. The first research direction develops a residual modeling framework that corrects systematic errors in physics-based models and reconstructs hidden dynamics in complex systems. By treating discrepancies between observed data and model predictions as learnable residuals, this approach enhances predictive accuracy and captures low-amplitude signals masked by dominant patterns. The framework is demonstrated in Electrocardiographic Imaging (ECGI), where it enables accurate cardiac modeling through both error correction and dynamic reconstruction. The second research direction advances Physics-Informed Neural Networks (PINNs) through meta-learning to enable rapid adaptation across diverse configurations. First, a Difficulty-Aware Task Sampler (DATS) is introduced to improve training efficiency by prioritizing tasks based on complexity, enabling PINNs to generalize effectively while reducing computational cost. Second, a meta-PINN framework for cardiac modeling is developed that leverages hypernetworks to generate patient-specific models, enabling fast personalization without retraining. Collectively, these contributions advance hybrid modeling by unifying physics-based and data-driven approaches, resulting in robust, interpretable models with improved computational efficiency. Extensive evaluations on simulated and real-world datasets demonstrate significant improvements in accuracy, adaptability, and computational efficiency over state-of-the-art approaches, strengthening the foundation of hybrid modeling and enabling interpretable, subject-specific models for complex, real-time applications in healthcare and beyond.

Publication Date

12-2025

Document Type

Dissertation

Student Type

Graduate

Degree Name

Computing and Information Sciences (Ph.D.)

Department, Program, or Center

Computing and Information Sciences Ph.D, Department of

College

Golisano College of Computing and Information Sciences

Advisor

Linwei Wang

Advisor/Committee Member

Laura Munoz

Advisor/Committee Member

Nathan Cahill

Campus

RIT – Main Campus

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