Fundamental governing physics and domain knowledge impose critical constraints on how data should be modeled and how models can be interpreted. This seminar presents some new methodologies that facilitate the integration of fundamental governing physics into data-driven models. Topics include (i) the statistical modeling for spatio-temporal advection-diffusion processes and nonlinear dynamical systems, as well as its applications in environment, energy, and structural dynamics (e.g., wildfires, solar energy, collision problems, etc.); (ii) inverse modeling and sensor placement; and (iii) adapting projection-based reduced-order models using Gaussian Processes.