CAREER: Towards Harnessing the Motility of Microorganisms: Fast Algorithms, Data-Driven Models, and 3D Interactive Visual Computing

由于体型较小，微生物认为液体比鱼或人类粘性大得多。这些小生物必须采取不同的策略才能有效地游泳。他们中的许多人通过摆动纤毛和鞭毛等微结构在液体中推进自己。微生物在周围流体中移动和导航的非凡效率促使人们最近建造了用于混合和运输的微流体设备，以及用于药物输送和细胞操纵的微型机器。由于理论分析和实验在这种情况下是具有挑战性的，数学建模和数值模拟在这些发展中变得不可或缺。该项目旨在创建改进的计算和可视化工具，以促进对微生物能动性的理解和我们驾驭这一过程的能力。该项目将开发一个交互式三维视觉计算系统，以作为(1)研究游泳微生物流体动力学的研究工具，(2)测试和改进人工、生物启发的微型游泳者设计的工程工具，以及(3)向各级学生介绍这一领域的教育工具。该项目还将为本科生和研究生、博士后研究人员和高中教师提供直接的培训和研究机会。该项目包括开发基于微泳者的虚拟现实游戏，将在科学与技术博物馆和公共图书馆展出。该项目的研究目标包括开发一种高效的、多网格式的方法来处理由相互作用的微型游泳者模拟产生的大而密集的矩阵，一种数据驱动的降阶模型来跟踪流体粒子，一种高效的数值方法来优化给定任务的仿生游泳者的设计，以及一个用于实时流体可视化和操纵的三维交互视觉计算系统。多重网格法利用了游泳者的几何学，因此有望比目前的数值方法更有效。人工神经网络将被用作流体颗粒位置变化的数据驱动的降阶模型。这种方法旨在非常有效地模拟流体颗粒的轨迹，因为它不需要计算流体-结构相互作用，这是实时和/或多查询场景中的一个重要方面。规划的数值优化方法既利用了遗传算法在寻找全局最优解时的可靠性，又利用了基于梯度的方法在给出良好的初始猜测时的效率。交互式视觉计算系统旨在作为一个虚拟实验室，用于分析参数变化的影响。该项目由数学科学部的计算数学和数学生物学项目共同资助。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Due to their small size, microorganisms perceive a fluid as much “stickier” than do fish or humans. Such small creatures must adopt a different strategy for efficient swimming. Many of them propel themselves in the fluid by wiggling micro-structures such as cilia and flagella. The remarkable efficiency of microorganisms at moving and navigating through a surrounding fluid has inspired recent construction of microfluidic devices for mixing and transport, and micro-machines for drug delivery and manipulation of cells. Since theoretical analyses and experimentation are challenging in this setting, mathematical modeling and numerical simulation have become indispensable in these developments. This project aims to create improved computational and visualization tools for advancing understanding of the motility of microorganisms and our capability to harness this process. The project will develop an interactive three-dimensional visual computing system to serve as (1) a research tool for studying the hydrodynamics of swimming microorganisms, (2) an engineering tool for testing and improving the design of artificial, bio-inspired micro-swimmers, and (3) an educational tool for introducing students of all levels to this field. The project will also provide direct training and research opportunities for undergraduate and graduate students, postdoctoral researchers, and high school teachers. The project includes plans to develop virtual reality games based on microswimmers to be exhibited at the Museum of Science & Technology as well as public libraries. Research objectives in this project include the development of an efficient, multigrid-like method for manipulating the large, dense matrices arising from the simulation of interacting micro-swimmers, a data-driven, reduced order model for tracking fluid particles, an efficient numerical method for optimizing the design of bio-inspired swimmers given a task, and a three-dimensional interactive visual computing system for real-time fluid visualization and manipulation. Multigrid methods exploit the geometry of the swimmers and are therefore expected to be more efficient than current numerical approaches. An artificial neural network will be leveraged as a data-driven, reduced order model for the change in a fluid particle’s position. This approach is intended to simulate a fluid particle's trajectory very efficiently, since it does not require calculating fluid-structure interactions, an important aspect in real-time and/or multi-query scenarios. The planned numerical optimization method takes advantage of both the reliability of a genetic algorithm at finding global optima and the efficiency of a gradient-based method when a good initial guess is given. The interactive visual computing system is intended to serve as a virtual laboratory for analysis of the effects of parameter changes. This project is jointly funded by the Computational Mathematics and the Mathematical Biology Programs of the Division of Mathematical Science.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.