Model Data Integration in Complex Dynamical Systems: Applications to Materials Synthesis

Many dynamical systems in science and engineering are described by mathematical models, often formulated as systems of ordinary or partial differential equations. These models, however, are only approximations of reality: they rely on idealized assumptions, simplified kinetics, and parameters that are often uncertain or unknown. As a result, accurately describing system behavior over time requires integrating these models with observational data, which is typically indirect, noisy, and incomplete. In this talk, I present a general framework for model data integration based on sequential Bayesian inference. I discuss how ensemble and score-based filtering methods address challenges related to high dimensionality, sparse observations, and the interpretation of dynamically inferred parameters. Finally, I illustrate the approach through an application to real-time joint state and parameter estimation in thin-film growth, where in-situ optical measurements are combined with kinetic models to infer the evolving system dynamics.