We focus on the modeling and analysis of dynamical systems using a combination of physics-informed machine learning, deep learning, and graph neural networks (GNNs). We focus on developing Physics-Informed Machine Learning (PIML) frameworks that integrate mechanistic models (e.g., Partial Differential Equations (PDEs), Ordinary Differential Equations (ODEs)) with data-driven techniques to enhance forecasting, robustness, and decision-making in complex systems. We also study the generalization capabilities of deep learning architectures, including neural ordinary differential equations (ODEs), to improve robustness in various tasks, including disease forecasting.