Algorithms, Theory, and Applications for Fiber Coating Systems

沿垂直纤维向下流动的薄液膜，一种称为纤维涂层的现象，是各种工程应用中的基本组成部分，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。这些液体膜自发地表现出有趣的界面不稳定性，导致列车的旅行液滴和不规则的波浪图案。尽管人们对纤维涂层动力学建模进行了广泛的研究，但这些模型固有的非线性和简并性往往在更广泛的应用中带来分析和计算挑战。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光纤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导致一个原型的实时模拟和预测在光纤涂层应用。该项目的部分内容将纳入调查员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具有挑战性的自由表面流动问题的理论和算法，这些问题来自光纤涂层系统。这些问题的特点是四阶高度非线性偏微分方程（PDE）系统，这是敏感的传统数值方法和数据驱动的机器学习方法。该项目的目标是围绕三个相互关联的方面：1）分析耦合PDE系统描述的液滴运动的规律性和结构。衍生的结构将被用来开发简化的动力系统，从全阶模型为个人液滴。将研究一个原型控制问题，为一般光纤涂覆系统的控制设计奠定基础; 2）开发鲁棒性和结构保持算法，用于模拟和学习光纤涂覆动力学。这涉及桥接基于物理的建模原理，PDE理论和神经常微分方程技术，用于长时间序列学习和降阶建模。该项目中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刚性物理系统的科学机器学习;（3）现实世界的大-该奖项反映了NSF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。

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.