TRIPODS+X:RES:Collaborative Research: Improving Templated Microstructures via Topological Data Analysis

微结构在材料科学中的重要性是公认的。它们的局部和全局几何形状在很大程度上影响着正在设计的材料的功能行为。因此，其受控制造方法一直是国内外研究的热点。现在，随着材料在更高分辨率和更快时间尺度上的表征的不断进步，对数据驱动的结构数字模拟和分析的需求越来越大。该项目专注于通过罗格斯大学材料和数据科学家与俄亥俄州立大学三脚架中心的数据科学家的合作，利用拓扑数据分析的新领域来推进模板微结构设计的设计。模板是这种协作的理想主题领域，因为它明确地指导了加工过程中的形状开发，并可以从更深层次的拓扑和统计分析中受益匪浅。研究人员将在材料科学、计算机科学和统计学之间开发一种与拓扑相关的协同效应，这将使使用模板改进材料加工成为可能。在本程序中开发的几何和拓扑方面的进展也有望扩展到材料加工的其他领域，每个领域都有独特的形状新颖性、对齐效果或纹理开发。该项目的工作还可能使一系列类似的应用领域受益，如医学图像分析、计算神经解剖学、地理信息系统和工程设计。事实上，在俄亥俄州立大学的三脚架中心，将几何/拓扑方法应用于其中一些其他应用领域的合作已经在进行中，并可能受益于与这个以材料为重点的程序的密切合作。拟议的研究涉及代数拓扑和几何的数学领域、应用统计学以及算法和图论的计算领域的概念。这些将应用于通过模板创建的材料微结构，以帮助理解拓扑互连、形状和动力学，这将有助于设备操作中的功能改进。拓扑数据分析的研究提出了在有限数据、近似和噪声存在的情况下研究拓扑概念的需要，这些约束总是在真实材料表征中遇到的。对有意结构化的材料进行几何和拓扑计算将产生大数据和多样化的数据，这些数据可以影响和改进未来的材料和器件制造工作。这些新的数据方法将引起拓扑界和统计界的兴趣，并为预测和有意创建具有增强功能的结构开辟新的途径。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。

The importance of microstructures in Material Science is well recognized. Their local and global geometry influence the functional behaviors of the materials being designed in a major way. Therefore, methodologies for their controlled manufacturing have always been a focus of intense research. Now, with continuing advancements in characterization of materials at higher resolution and faster time scales there is intensified need for data driven digital simulation and analysis of structure. This project focuses on leveraging the new area of topological data analysis in advancing the design of templated microstructure designs through a collaboration between material and data scientists at Rutgers University and data scientists at the TRIPODS center at Ohio State University. Templating is the ideal topical area for this collaboration because it so definitively directs shape development during processing and can benefit greatly from deeper topological and statistical analytics. The researchers will develop a topology-related synergy between Materials Science, Computer Science, and Statistics that will enable improved processing of materials using templating. The geometrical and topological advances developed in this program are expected to also be extensible to other areas of materials processing, each of which has unique shape novelty, alignment effects, or texture development. The project's work could also benefit a range of similar application fields such as medical image analysis, computational neuroanatomy, geographic information systems, and engineering designs. Indeed, collaborations to apply geometric/topological methods to some of these other application fields are already underway at the TRIPODS center at OSU and could benefit from close collaboration with this Materials-focused program as it develops.The proposed research involves concepts from mathematical areas of algebraic topology and geometry, applied statistics, and computational areas of algorithms and graph theory. These will be applied to materials microstructures created by templating to help understand topological interconnections, shapes, and dynamics, which would be of benefit to functional improvements in device operation. Research in topological data analysis has brought forth the need to investigate topological concepts in the presence of finite data, approximations, and noise, constraints that are always encountered in real materials characterization. Geometric and topological computation with intentionally structured materials will yield big and diverse data that can influence and improve future material and device fabrication efforts. These new data methods will be of interest to the topological and statistical communities as well as open up new avenues for predicting and intentionally creating structures with enhanced functionality.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.