DMREF: Deblurring our View of Atomic Arrangements in Complex Materials for Advanced Technologies

DMREF：模糊我们对先进技术复杂材料中原子排列的看法非技术性描述：当我们尝试寻找新技术来解决人类面临的一些最严峻的挑战（例如丰富的可持续能源、环境修复和健康）时，我们越来越多地寻求越来越复杂的材料。 我们已经拥有将阳光转化为电能的设备，并利用阳光将水分解成珍贵的氢燃料，但设备效率和成本等问题意味着当前的技术无法达到我们现代需求所需的大规模。这个难题可以通过使用先进材料来解决，这些材料可以以更高的效率执行其任务——能量转换、癌细胞杀手或其他任何可能的任务。 这不可避免地导致我们走向更复杂的材料，这些材料由许多不同的化学元素组成，并在从原子到纳米和介观尺度一直到宏观尺度的多个不同长度尺度上设计结构。 问题是，由于它们的复杂性，当我们制造出这些材料时，甚至很难对其进行表征，更不用说在纳米尺度上设计和工程它们了。 我们常用的基于晶体散射 X 射线的工具不适用于这种纳米级结构。 问题不在于我们缺乏足够强大的 X 射线束。 问题在于，这些复杂材料的 X 射线散射信号不包含足够的信息，无法让我们找到独特的结构解决方案。 就好像我们正在通过模糊的、冒着蒸汽的眼镜观察原子排列的复杂模式。 该项目将通过结合图像识别、信息论和机器学习等不同领域的应用数学进展（这些领域对商业、执法等产生变革性影响），并将其应用于识别最复杂材料中的原子排列问题，使这一情况更加清晰。技术描述：该方法将通过将纳米材料 X 射线散射数据处理的最新进展（例如原子对分布函数 (PDF) 分析）与其他输入源结合起来，解决材料的多尺度结构。小角度散射、EXAFS 和其他光谱学等信息，以及来自 DFT 等第一原理理论的输入，但将它们置于严格的数学框架和强大的计算框架中，以便最大程度地利用数据中的信息内容，同时考虑统计和系统不确定性的不确定性。 该数学框架将利用随机优化、不确定性量化（包括函数空间贝叶斯方法）、机器学习和图像识别方面的最新进展。

DMREF: Deblurring our View of Atomic Arrangements in Complex Materials for Advanced TechnologiesNon-technical Description: As we try and find new technologies to solve some of mankind's toughest challenges such as abundant sustainable energy, environmental remediation, and health, we are increasingly seeking more and more complex materials. We already have devices that turn sunlight into electricity and use sunlight to split water into precious hydrogen fuel, but issues such as device efficiency and cost mean that the current technologies cannot be taken to the vast scale needed for our modern needs. This puzzle may be solved by the use of advanced materials that perform their tasks - energy conversion, cancer cell killer, or whatever it may be - with greater efficiency. This is inevitably leading us towards more complicated materials that consist of many different chemical elements and have engineered structures on multiple different length-scales from the atomic to the nano- and meso-scales all the way to macroscopic scales. The problem is that, because of their complexity, it becomes very difficult to even characterize these materials when we have made them, let alone design and engineer them at the nanoscale. Our usual tools based on the scattering of x-rays by crystals stop working for such nanoscale structures. The problem is not that we lack powerful enough x-ray beams. The problem is that the x-ray scattering signal from these complicated materials doesn't contain enough information to allow us to find a unique structure solution. It is as if we are looking at complex patterns of atomic arrangements through blurry, steamed up glasses. This project will bring greater clarity to this situation by marrying together advances in applied mathematics from diverse areas such as image recognition, information theory and machine learning, which are having transformative impacts in commerce, law enforcement and so on, and applying them to the problem of recognizing atomic arrangements in materials of the highest complexity.Technical Description: The approach will to solve multi-scale structures of materials by marrying together the latest advances in the processing of x-ray scattering data from nanomaterials, such as atomic pair distribution function (PDF) analysis, with other sources of input information such as small angle scattering, EXAFS and other spectroscopies, as well as inputs from first principle theory such as DFT, but place them in a rigorous mathematical framework and a robust computational framework such that the information content in the data may be utilized to the greatest extent possible whilst taking into account uncertainties from statistical and systematic uncertainties. The mathematical framework will utilize the latest developments in stochastic optimization, uncertainty quantification including function-space Bayesian methods, machine learning and image recognition.