DELTA: Descriptors of Energy Landscape by Topological Analysis

二十年前，机器学习（ML）开始了理论/算法改进的轨迹，这些改进导致了先进的能源效率材料和分子机器，这些机器以人类无法理解的方式合成分子。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-将代数拓扑与计算方法相结合，通过表征数据的全局形状来提取新知识。华盛顿州立大学的Clark教授、科罗拉多州立大学的Adam教授、科罗拉多大学博尔德分校的Pflaum教授、伦斯勒理工学院的Sundararaman教授和伊利诺伊大学厄巴纳香槟分校的张教授正在开发科学与工程数据密集型研究所--题为“使用拓扑数据分析的能源景观描述符”（DELTA）的框架。 他们正在致力于推进TDA，以研究化学中发现的密集和复杂的数据集，重点是开发方法和软件工具，以表征化学转化过程中描述能量流的功能，称为能量景观。可扩展和可扩展的TDA工具用于从能源格局中提取新信息，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，包括实时优化和控制化学系统的长期挑战。在数学、数据科学和化学的交叉点上，在DELTA及其合作伙伴的帮助下培养的学生为新的实践社区奠定了技能和基础。化学家通常不知道转化的潜在能量景观如何作为系统条件的函数而变化，也不知道分子内和分子间相互作用及其拓扑特征之间存在可量化的关系。拓扑数据分析（TDA）是从能源景观（EL）中提取新信息的独特方法，因为它将代数拓扑与计算方法相结合，以表征其数据的全局形状。使用拓扑数据分析的能源景观描述符（DELTA）研究所框架将TDA应用于化学应用，调用持久同源性，莫尔斯理论，突变理论和其他拓扑描述符，并创建新的软件工具，可由领域专家访问。处理3 N维能量表面需要可扩展和可扩展的工具，首先降低其维数（目标1），然后产生几何和拓扑描述符，量化EL在不同化学条件下扰动的方式（目标2）。这为加速EL大区域采样的新预测方法提供了基础，并且已经学会了如何优化景观拓扑结构以控制反应分子和相行为的命运（目标3）。该项目是国家科学基金会利用数据革命大创意活动的一部分。该奖项由NSF数学和物理科学理事会化学部共同资助。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值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.