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

该奖项全部或部分由《2021年美国救援计划法案》（公法117-2）资助。非牛顿流体的精确建模是计算数学中的一个长期挑战，在流体物理、化学工程和材料科学的基本扩散、输运和合成过程的预测和控制中起着核心作用。与简单流体不同，由于溶质动力学的多尺度性质，非牛顿流体往往表现出复杂的流动行为；一般来说，标准物理定律失效了。传统的流体动力学模型通常基于微观尺度相互作用的经验近似，这需要仔细调整参数，并且通常显示保持分子水平保真度的能力有限。这种差距严重限制了对多尺度输运平衡规律的基础科学理解和相关工程应用中的预测控制。该项目旨在开发一种新的机器学习计算工具，直接从微观尺度描述中构建精确和能量稳定的非牛顿流体动力学模型。正在开发的模型将编码非均质分子水平的相互作用，并能够对软物质、聚合物液体和囊泡悬浮液等多尺度流体进行预测建模，而经验模型在这些领域存在局限性。该项目的教育部分将为高中生、本科生和研究生提供一套跨学科培训和推广活动，以促进计算数学和自然科学界面的数据科学教育。机器学习和计算数学之间的直接联系旨在为这个快速发展的领域的下一代STEM劳动力提供真正的跨学科培训，并吸引和留住数学界的不同学生群体。该项目还将利用与斯佩尔曼学院现有的联合项目，为对该领域感兴趣的代表性不足的学生建立一个支持网络。该研究项目旨在提供一种学习高保真度和真正可靠的多尺度流体系统计算模型的新方法。主要的创新将是在没有经验近似的情况下将微观尺度的相互作用无缝地传递到宏观尺度动力学的能力。与一些基于机器学习的建模结果相比，所得到的模型将保留嵌入基本能量形式的清晰物理解释，而不是简化动力学的黑盒拟合，并将保证能量稳定。此外，学习算法将只需要离散而不是时间序列样本，并且非常适合实际应用。该方法旨在为中尺度输运平衡定律的基础科学理解提供一种独特的方法，在中尺度输运平衡定律中，规范的斯托克斯-爱因斯坦方程失效了。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

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.