Divide-and-Conquer Approach for Strongly Interacting Systems via Convex Optimization

通过凸优化的强交互系统的分而治之方法

• 批准号: 2111563
• 负责人: Yuehaw Khoo
• 金额: $ 22.5万
• 依托单位: University of Chicago
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2021
• 资助国家: 美国
• 起止时间: 2021-07-01 至 2024-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2111563&HistoricalAwards=false
• 关键词: Divide; Conquer; Approach; Strongly; Interacting

Many problems in physics, data science and engineering involve interactions of so-called agents via pairwise potentials. Beyond the simple regime where the agents are independent of each other, determining the joint states of agents often suffers from complexity that increases quickly with the dimension of the problem; this feature is called the curse-of-dimensionality. Research in this project will address these challenges by exploiting a convex optimization approach and will demonstrate synergy between various aspects of computational mathematics and data science. The project will provide new tools for the Material Genome Initiative by accelerating the computation of many-body quantum system as well as improve the capability of protein structure determination from distance-based experimental measurements. Graduate students will be involved in research and will receive interdisciplinary training. The project will develop a variety of divide-and-conquer and multiscale techniques to significantly improve the scalability of algorithms for interacting agents. In addition, tensor compression strategies will be developed to accelerate the solution of subproblems. The project will demonstrate the effectiveness of the strategy for several scenarios. In the domain of data science, through the lens of the proposed optimization methods, the PI will investigate the sensor-network localization problem and multimarginal optimal transport problem. In physics and chemistry, alternative paradigms will be developed for solving for the ground state energy of strongly correlated systems such as quantum Ising and Hubbard models.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.

物理学、数据科学和工程学中的许多问题都涉及所谓的代理通过成对势的相互作用。除了智能体​​彼此独立的简单机制之外，确定智能体的联合状态通常会遇到复杂性，这种复杂性会随着问题的规模而迅速增加。这个特征被称为维数灾难。该项目的研究将通过利用凸优化方法来解决这些挑战，并将展示计算数学和数据科学各个方面之间的协同作用。该项目将通过加速多体量子系统的计算以及提高基于距离的实验测量确定蛋白质结构的能力，为材料基因组计划提供新工具。研究生将参与研究并接受跨学科培训。该项目将开发各种分而治之和多尺度技术，以显着提高交互代理算法的可扩展性。此外，还将开发张量压缩策略来加速子问题的解决。该项目将展示该策略在多种情况下的有效性。在数据科学领域，通过所提出的优化方法的镜头，PI 将研究传感器网络定位问题和多边际最优传输问题。在物理和化学领域，将开发替代范式来解决强相关系统的基态能量，例如量子伊辛和哈伯德模型。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力优点和能力进行评估，被认为值得支持。更广泛的影响审查标准。