Algorithms, Theory, and Applications for Fiber Coating Systems

沿着垂直纤维向下流动的液体薄膜，这种现象被称为纤维涂层，是各种工程应用的基本组成部分，例如用于热脱盐、水蒸气和超细颗粒捕获的质量和热交换器。这些液体薄膜自发地表现出有趣的界面不稳定性，导致行进的液滴和不规则的波浪图案。尽管对纤维涂层动力学建模已经有了广泛的研究，但这些模型固有的非线性和简并性在更广泛的应用中经常给分析和计算带来挑战。该研究项目旨在开发一种混合数值和机器学习框架，以加速计算并促进与纤维涂层系统相关的大规模刚性问题的控制。这些技术的发展可以为光纤涂层应用的实时模拟和预测提供一个原型。该项目的部分内容将被纳入研究者的科学计算和数据科学课程。该项目还将为本科生和研究生提供研究培训机会。该项目将采用分析方法、数值模拟和机器学习技术来开发理论和算法，以解决纤维涂层系统中出现的具有挑战性的自由表面流动问题。这类问题的特点是四阶高非线性偏微分方程（PDE）系统，它对传统的数值方法和数据驱动的机器学习方法很敏感。该项目的目标围绕三个相互关联的方面进行组织：1)分析耦合PDE系统描述的旅行液滴的规律性和结构。推导的结构将用于从单个液滴的全阶模型开发简化的动力系统。研究原型控制问题，为通用纤维涂层系统的控制设计奠定基础；2)开发用于模拟和学习纤维涂层动力学的鲁棒和结构保持算法。这包括连接基于物理的建模原理、PDE理论和神经常微分方程技术，用于长时间顺序学习和降阶建模。本项目为高阶非线性退化偏微分方程开发的数据驱动学习技术有望推进硬物理系统的科学机器学习；3)现实世界的大规模应用将作为理论理解和验证所开发算法的案例研究。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。

Thin liquid films flowing down a vertical fiber, a phenomenon known as fiber coating, is a fundamental component in various engineering applications such as mass and heat exchangers for thermal desalination, water vapor, and ultra-fine particle capture. These liquid films spontaneously exhibit intriguing interfacial instabilities, leading to trains of traveling droplets and irregular wavy patterns. Although there have been extensive studies on the modeling of fiber coating dynamics, the inherent nonlinearity and degeneracy of these models often present analytical and computational challenges in broader applications. This research project aims to develop a hybrid numerical and machine learning framework that accelerates the computation and facilitates the control of large-scale stiff problems associated with fiber coating systems. The development of these techniques can lead to a prototype for real-time simulation and prediction in fiber coating applications. Parts of the project will be incorporated into the investigator’s courses on scientific computing and data science. This project will also provide research training opportunities for both undergraduate and graduate students. This project will employ analytical approaches, numerical simulations, and machine learning techniques to develop theory and algorithms for challenging free-surface flow problems that arise from fiber coating systems. Such problems are characterized by fourth-order highly-nonlinear partial differential equation (PDE) systems, which are sensitive to traditional numerical methods and data-driven machine-learning approaches. The objectives of the project are organized around three interconnected aspects: 1) Analysis of the regularity and structure of traveling droplets described by coupled PDE systems. The derived structures will be utilized to develop simplified dynamical systems from full-order models for individual droplets. A prototype control problem will be studied to establish the foundation for control design of general fiber coating systems; 2) Development of robust and structural-preserving algorithms for simulating and learning fiber coating dynamics. This involves bridging physics-based modeling principles, PDE theory, and neural ordinary differential equation techniques for long-time sequential learning and reduced-order modeling. The data-driven learning techniques developed for high-order nonlinear degenerate PDEs in this project are expected to advance scientific machine learning for stiff physical systems; 3) A real-world large-scale application will serve as a case study for the theoretical understanding and verification of the developed algorithms.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.