CDS&E/Collaborative Research: The Integration of Data-Mining with Multiscale Engineering Computations

这一合作研究项目旨在开发数学方法，用于分析/挖掘工程/物理化学计算中出现的大规模高维数据，更重要的是，利用这些方法和算法来加速计算本身。数据挖掘和科学计算之间的这种类型的协同有可能显著提高我们从大规模建模和模拟中提取知识的方式。该方法的重点是发现以大量自由度为特征的模拟的少量关键的内在特征，并利用这些关键特征来系统地设计后续的模拟。这项工作的另一个重要特点是开发了在精细、详细和粗略、紧凑的数据描述之间“转换”的算法，以及在以前的计算框架中快速纳入新数据/信息的算法。这项工作的成果将是算法本身，以及它们在大规模分子和基于试剂的模拟中应用的有文件记录的说明性例子。如果成功，这项研究将创建、记录并提供一个计算协议，以加强复杂动态系统建模中的大规模科学计算。应用的例子包括纳米级自组装，如材料计算中的胶束形成、大分子折叠、生态学和细胞生物学中基于大规模试剂的集体运动模型，以及对燃烧等工程问题的大规模偏微分方程模拟。这些结果将被传播，以供其他研究人员使用。这项研究将构成工程和数学研究生跨学科教育的基础，以及这些学科的本科生研究项目的基础。它还将为大规模数据处理课程材料的开发奠定基础。

This collaborative research project aims at developing mathematical methods for the analysis/mining of large scale, high dimensional data that arise in engineering/physicochemical computations, and, more importantly, in exploiting these methods and algorithms to accelerate the computations themselves. This type of synergy between data mining and scientific computation has the potential to significantly enhance the way we extract knowledge from large scale modeling and simulation. The focus of the approach is the discovery a small number of key, intrinsic features of simulations characterized by very large numbers of degrees of freedom - and the exploitation of these key features to systematically design subsequent simulations. Another important feature of the work is the development of algorithms that "translate" between fine scale, detailed, and coarse scale, compact descriptions of the data, as well as algorithms for the fast incorporation of new data/information in previous computational frameworks. Deliverables of the effort will be the algorithms themselves, as well as documented illustrative examples of their application to large scale molecular and agent-based simulations.If successful, this research will create, document and make available a computational protocol for enhancing large scale scientific computations in the modeling of complex dynamical systems. Example applications include nanoscale self-assembly, such as micelle formation in materials computations, macromolecular foldling, large scale agent-based models of collective motion in ecology and cellular biology, as well as large scale, Partial Differential Equation simulations of engineering problems, like combustion. The results will be disseminated to allow their use by other researchers. The research will form the basis of cross-disciplinary education of graduate students in engineering and in mathematics, and of undergraduate research projects in these disciplines. It will also underpin the development of course materials in large scale data processing.