Multi-scale modeling presents a long-standing challenge in computational mathematics and is pertinent to a wide range of applications in materials science, fluid physics, and chemical engineering. Predicting collective behaviors typically necessitates the integration of modeling dynamics across micro-scale (atomistic), meso-scale (kinetic), and macro-scale (continuum) levels, with the vast range of spatiotemporal scales posing a fundamental obstacle. Existing methods often rely on certain empirical constitutive closures or micro-macro coupling approaches. Despite their broad applications, modeling accuracy and efficiency are often challenged in real applications. This dissertation aims to develop data-driven approaches for constructing accurate and reliable reduced models of multi-scale systems based on first-principle descriptions. The first part, including Chapters 2 and 3, focuses on constructing meso-scale reduced models of polymer kinetics directly from the full molecular dynamics. Chapter 2 discussed the many-body effect on conservative force, which is important to accurately reproduce both the probability density function of the void formation in bulk and the spectrum of the capillary wave across the fluid interface. Chapter 3 discussed the state-dependence on memory kernel and demonstrated the essential role of the broadly overlooked state-dependency nature in predicting molecule kinetics related to conformation relaxation and transition. The second part, Chapter 4, focuses on building accurate macroscale models from microscale polymer kinetics through meso-scale Langevin dynamics. A non-Newtonian hydrodynamic model is given as an example, which shows some success in systematically passing the micro-scale heterogeneous polymer structural mechanics to the macro-scale hydrodynamics without human intervention.
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