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

微观结构在材料科学中的重要性是众所周知的。它们的局部和全局几何形状主要影响所设计材料的功能行为。 因此，其控制生产的方法一直是激烈的研究的焦点。现在，随着材料表征在更高分辨率和更快时间尺度上的不断进步，对数据驱动的数字模拟和结构分析的需求越来越大。该项目的重点是利用拓扑数据分析的新领域，通过罗格斯大学的材料和数据科学家与俄亥俄州州立大学TRIPODS中心的数据科学家之间的合作，推进模板化微结构设计的设计。模板是这种合作的理想主题领域，因为它在加工过程中明确指导形状开发，并且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作用，从而能够使用模板改进材料的处理。该计划中开发的几何和拓扑进步预计也可扩展到材料加工的其他领域，每个领域都具有独特的形状新奇，对齐效果或纹理发展。 该项目的工作也可以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，合作应用几何/拓扑方法的一些其他应用领域已经在俄勒冈州立大学的TRIPODS中心正在进行中，并可能受益于密切合作，这一材料为重点的程序，因为它development.The拟议的研究涉及代数拓扑和几何的数学领域的概念，应用统计，算法和图论的计算领域。这些将被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，这将有利于器件操作中的功能改进。 在拓扑数据分析的研究提出了需要调查的有限数据，近似和噪音，总是遇到在真实的材料表征的约束的存在下的拓扑概念。有意结构化材料的几何和拓扑计算将产生大量不同的数据，这些数据可以影响和改善未来的材料和器件制造工作。这些新的数据方法将是感兴趣的拓扑和统计社区，以及开辟新的途径，预测和故意创造结构与增强的功能。这个奖项反映了NSF的法定使命，并已被认为是值得的支持，通过评估使用基金会的知识价值和更广泛的影响审查标准。

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.