CAREER: Machine-Learning Construction of Energy-Stable Non-Newtonian Fluid Hydrodynamics with Molecular Fidelity

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This award is funded in whole or in part under the American Rescue Plan Act of 2021 (Public Law 117-2). Accurate modeling of non-Newtonian fluids is a longstanding challenge in computational mathematics, and plays a central role in the prediction and control of the fundamental diffusion, transport, and synthesis processes in fluid physics, chemical engineering, and materials science. Unlike simple fluids, non-Newtonian fluids often exhibit complex flow behaviors arising from the multiscale nature of the solute dynamics; canonical physical laws break down in general. Conventional hydrodynamic models are often based on empirical approximations of the microscale interactions, which require careful parameter tuning and generally show limited capability to retain molecular-level fidelity. This gap severely limits both the fundamental scientific understanding of multiscale transport balance laws and the predictive control in relevant engineering applications. This project aims to develop a new machine-learning computational tool to construct accurate and energy-stable non-Newtonian hydrodynamic models directly from the micro-scale descriptions. The models under development will encode heterogeneous molecular-level interactions and enable predictive modeling of multiscale fluids such as soft matter, polymeric liquids, and vesicle suspensions, where empirical models show limitations. The educational part of the project will provide a suite of interdisciplinary training and outreach activities for high school, undergraduate, and graduate students to promote data science education at the interface of computational mathematics and natural sciences. The direct connection between machine learning and computational mathematics is intended to provide truly interdisciplinary training for the next generation of the STEM workforce in this fast-growing field and to attract and retain a diverse population of students in the mathematics community. The project will also leverage an existing joint program with Spelman College to build a network of support for underrepresented students with interest in this field. The research project aims to deliver a novel approach for learning high-fidelity and truly reliable computational models of multiscale fluid systems. The main innovation will be the capability to seamlessly pass the microscale interactions to the macroscale dynamics without empirical approximations. In contrast to the results of some machine-learning-based modeling, the resulting model will retain a clear physical interpretation embedded with a fundamental energy form rather than a black-box fit of reduced dynamics and will be guaranteed to be energy stable. Moreover, the learning algorithm will only require discrete rather than time-series samples, and be well-suited for practical applications. The method aims to provide a unique approach to fundamental scientific understanding of the mesoscale transport balance law where the canonical Stokes-Einstein equation breaks down.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.