Machine-Learning-Based Modeling of Multiscale Dynamic Systems with Non-Markovian State-Dependent Memory

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Accurate modeling of multiscale dynamic systems has been a long-standing problem that has attracted tremendous interest in computational mathematics and applications in fluid physics, chemical engineering, and materials science. The focus of this project is on multiscale systems that do not have clear scale separation, such as nanoscale multi-physics systems. For such systems the existing approaches feature so-called memory effects and non-Markovian behavior, which limit their understanding and control. The project will develop new advanced computational tools based on machine learning to construct highly accurate models of multiscale systems directly from first-principle-based descriptions. The constructed models retain a molecular-level fidelity and can be broadly applied to investigate the dynamic processes relevant to material design, drug delivery, and soft matter assembly. This project will also provide interdisciplinary training and research experiences for both graduate and undergraduate students. The research in this project will address a fundamental problem in model reduction and multiscale modeling for dynamic systems without clear scale separation. Current empirical models generally show limitations to retain the microscale level fidelity due to the over-simplification of the state-dependent Markovian memory term arising from the unresolved dynamics on microscale. This gap can be bridged by the methods based on machine-learning developed in this project; these will provide a general framework to learn a set of non-Markovian features from the full descriptions, and simultaneously, train the stochastic reduced model by embedding the state-dependent memory term in the extended dynamics of the non-Markovian features. Different from the conventional machine learning approaches for modeling dynamic equations, the models developed in this project are based on rigorous projection formalism and retain a clear physical interpretation. Consistent noise terms can be naturally introduced to the reduced models, which are well-suited for studying complex dynamic systems out of equilibrium. As a result, the methods can be employed to investigate open scientific questions such as the nanoscale assembly process by faithfully accounting for the microscale interactions. In the long term, this project will provide more comprehensive computational tools for establishing predictive modeling and control of such systems.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.