DELTA: Descriptors of Energy Landscape by Topological Analysis

20年前，机器学习(ML)开始了理论/算法改进的轨道，导致了用于能源效率的先进材料和以人类手无法理解的方式合成分子的分子机器。这些关键进展是基于统计方法的基础，这些方法现在反映了拓扑数据分析(TDA)领域--它将代数拓扑学与计算方法相结合，通过表征数据的整体形状来提取新的知识。华盛顿州立大学的Clark教授、科罗拉多州立大学的Adam教授、科罗拉多博尔德大学的Pflum教授、伦斯勒理工学院的Sundararaman教授和伊利诺伊大学Urbana Chample大学的张教授正在发展科学与工程数据密集型研究研究所--框架“使用拓扑数据分析描述能源景观”(Delta)。他们正在努力推进TDA，以研究在化学中发现的密集和复杂的数据集，方法和软件工具的开发，以表征描述化学转化过程中的能量流动的功能，即所谓的能量景观。可扩展和可扩展的TDA工具用于从能源环境中提取新信息，了解它在不同应用条件下如何变化，并支持化学中的新范式，包括化学系统实时优化和控制的长期挑战。在数学、数据科学和化学的交叉点，在Delta及其合作伙伴的培训下接受培训的学生开发新的实践社区的技能和基础。化学家通常不知道潜在的能量格局如何随着系统条件的变化而变化，也不知道分子内和分子间相互作用与其拓扑特征之间存在可量化的关系。拓扑数据分析(TDA)结合了代数拓扑学和计算方法来表征其数据的全局形状，是从能量景观(EL)中提取新信息的唯一准备。使用拓扑数据分析(Delta)研究所框架的能源景观描述符将TDA应用于化学应用，调用了持久同调、莫尔斯理论、突变理论和其他拓扑描述符，并创建了领域专家可以访问的新软件工具。处理3N维能面需要可伸缩和可扩展的工具，这些工具首先降低其维度(目标1)，然后产生几何和拓扑描述符，量化在不同化学条件下EL被扰动的方式(目标2)。这为新的预测方法提供了基础，这些方法加快了对EL大片区域的采样，并且已经学会了如何优化地形拓扑以控制反应分子的命运和相行为(目标3)。该项目是美国国家科学基金会利用数据革命大创意活动的一部分。这项工作是由NSF数学和物理科学局内的化学部共同资助的。这一奖项反映了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。

Twenty years ago, machine learning (ML) began a trajectory of theoretical/algorithmic improvements that have led to advanced materials for energy efficiency and molecular machines that synthesize molecules in ways unfathomable by the human hand. Those key advances were based upon a foundation of statistical methods that now mirror the field of topological data analysis (TDA) - which combines algebraic topology with computational methods to extract new knowledge by characterizing the global shape of data. Professor Clark at Washington State University, Professor Adam at Colorado State, Professor Pflaum at University Colorado Boulder, Professor Sundararaman at Rensselaer Polytechnic Institute, and Professor Zhang at University of Illinois Urbana Champagne are developing the Institute for Data-Intensive Research in Science and Engineering - Frameworks entitled "Descriptors of Energy Landscapes Using Topological Data Analysis" (DELTA). They are working on advancing TDA for the study of intensive and complex data sets found in Chemistry by focusing upon the development of methods and software tools that characterize the function that describes energy flow during chemical transformations, known as the energy landscape. Scalable and extensible TDA tools are used to extract new information from the energy landscape, understanding how it changes under different applied conditions and supporting a new paradigm in Chemistry, including the long-standing challenge of real-time optimization and control of chemical systems. At the intersection of Math, Data Science, and Chemistry, students trained under DELTA and its collaborative partners develop the skills and the foundation for a new community of practice.Chemists generally do not know how the underlying energy landscape of transformation changes as a function of system conditions, nor are there quantifiable relationships between intra- and intermolecular interactions and its topological features. Topological data analysis (TDA) is uniquely poised to extract new information from the energy landscape (EL), as it combines algebraic topology with computational methods to characterize its global shape of data. The Descriptors of Energy Landscapes Using Topological Data Analysis (DELTA) Institute Frameworks adapts TDA for chemistry applications, invoking persistent homology, Morse theory, catastrophe theory, and other topological descriptors and creating new software tools that are accessible by domain experts. Tackling the 3N-dimensional energy surface necessitates scalable and extensible tools that first reduce its dimensionality (Objective 1), then yield geometric and topological descriptors that quantify the way in which the EL is perturbed under different chemical conditions (Objective 2). This provides the basis for new predictive methods that accelerate sampling of large regions of the EL and have have learned how to optimize landscape topology to control the fate of reacting molecules and phase behavior (Objective 3). This project is part of the National Science Foundation's Harnessing the Data Revolution Big Idea activity. The effort is jointly funded by the Division of Chemistry within the NSF Directorate for Mathematical and Physical Sciences.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.