Algorithms and Computation for Rare Events in Complex Systems

该项目关注与平衡，亚稳态和过渡态的模拟和分析相关的数学和计算问题，以及实际利益的复杂能源景观的最小能量路径，以及相关的随机动力学。要进行的研究是密切的动机，在一些领域的应用程序的联邦战略利益：有效的算法和代码的发展是高性能计算的一个重要组成部分，和数值方法和软件工具的开发可能是潜在的有用的有效的计算材料和药物设计。首席研究员将开展跨学科研究，包括计算数学，物理，信息，材料和生物科学等学科。他将专注于新的算法开发和分析，这些算法有可能显着改善罕见事件建模和模拟的常规实践。他将考虑一些具体的和重要的应用，包括相互作用的粒子和界面的几何限制和挫折配置或变形的几何形状，出现在物理，化学和生物学的许多领域（如纳米簇的形成，双分子构象，囊泡介导的相互作用，和临界成核固态转换）的系统。他将试图与从业者在现有软件代码中开发的一些算法建立强有力的联系，例如第一原理计算和计算化学。 研究项目中涉及的大多数问题都与无限维空间（如确定性或随机偏微分方程）或高维有限维空间（微分方程的离散化或涉及大量粒子的粒子系统）相关，这导致了许多计算挑战。将研究各种数学和数值问题，从有效的局部鞍点搜索及其强大的数值实现，到相关动态和罕见事件的严格分析和有效的多尺度模拟。预计该项目期间取得的进展将对有兴趣研究罕见事件的社区产生广泛影响。该项目还将有助于教育和培训，因为它将为学生提供跨学科环境中的宝贵培训场所和研究经验。将大力促进各级学生的积极参与，并将研究结果纳入教学和培训。

The project is concerned with mathematical and computational issues related to the simulation and analysis of equilibria, metastable and transition states and minimum energy paths for complex energy landscapes of practical interests, and associated stochastic dynamics. The research to be carried out is closely motivated by applications in a number of areas of federal strategic interests: the development of effective algorithms and codes is a crucial part of high-performance computing, and numerical methods and software tools to be developed may be potentially useful for effective computational materials and drug design. The principal investigator will carry out interdisciplinary research that encompassing subjects like computational mathematics, physics, information, materials and biological sciences. He will focus on new algorithmic development and analysis which have the potential to significantly improve the usual practice on the modeling and simulation of rare events. He will consider some specific and important applications, including systems of interacting particles and interfaces in geometrically confined and frustrated configurations or deformable geometry which arise in many areas of physics, chemistry and biology (such as formation of nano-clusters, bimolecular conformation, vesicle mediated interactions, and critical nucleation in solid state transformations). He will attempt to draw strong connections with some of the algorithms developed by practitioners implemented in existing software codes such as those for first principle calculation and computational chemistry. Most of the problems involved in the research project are associated with either infinite dimensional spaces such as deterministic or stochastic partial differential equations or finite dimensional spaces with high dimensions (discretization of differential equations or particle systems involving a large number of particles), which lead to many computational challenges. Various mathematical and numerical issues will be studied, ranging from efficient local saddle point search and its robust numerical implementation to rigorous analysis and effective multiscale simulations of relevant dynamics and rare events. It is expected that the progress made during the project will have a broad impact on the community interested in the study of rare events. The project will also contribute to education and training as it will provide students valuable training ground and research experience in an interdisciplinary environment. Much effort will be devoted to promoting active engagement of student participation at all levels and integrating research findings into teaching and training.