AF: Small: Density Estimation and Uncertainty Propagation in Complex Systems

AF：小：复杂系统中的密度估计和不确定性传播

• 批准号: 1420882
• 负责人: Narayana Aluru
• 金额: $ 40万
• 依托单位: University of Illinois at Urbana-Champaign
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2014
• 资助国家: 美国
• 起止时间: 2014-08-01 至 2018-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1420882&HistoricalAwards=false
• 关键词: AF; Small; Density; Estimation; Uncertainty

Complex systems, involving coupled interactions among several disciplines, at micro and nanoscales are building blocks for many application areas including information technology, energy, and health sectors. Many of the advances in data revolution are due to the high quality images and information acquired by miniaturized sensors and their networks and this advanced sensor technology is an example of a complex system involving several interacting disciplines. A major bottleneck currently facing the design and operation of complex systems at small scales is the presence of uncertainties. Uncertainties such as variations in physical/material properties, geometry, applied signals, etc. cannot be avoided at small scales.  These uncertainties can significantly affect the performance of complex systems sometimes negating the performance merits of small scale systems. As a result, it is important to design complex systems in the presence of uncertainties. In this project, the PI plans to develop efficient and accurate algorithms for stochastic analysis of complex systems at small scales. The project aims to make algorithmic advances in three areas of relevance to stochastic analysis of complex systems. The first area involves development of kernel moment matching techniques to estimate probability density functions (pdfs) of uncertain inputs. The key idea is to estimate the pdf such that the output statistics are optimized. The second area involves development of algorithms for numerical analysis of stochastic mathematical models governing complex systems. The third area involves development of integrated data-driven stochastic algorithms for coupled analysis of complex systems. The integrated stochastic environment will be used not only for robust design of complex systems but also to explore design and development of novel complex systems.Graduate and undergraduate students, including women and under-represented students, will be trained in the interdisciplinary area involving algorithms, physics and engineering.

在微观和纳米尺度上，涉及多个学科之间耦合相互作用的复杂系统是许多应用领域的基石，包括信息技术、能源和卫生部门。数据革命的许多进步是由于小型化传感器及其网络所获得的高质量图像和信息，这种先进的传感器技术是涉及多个相互作用的学科的复杂系统的一个例子。目前，小尺度复杂系统的设计和运行面临的一个主要瓶颈是不确定性的存在。不确定性，如物理/材料特性、几何形状、应用信号等方面的变化，在小尺度上是无法避免的。这些不确定性会严重影响复杂系统的性能，有时会抵消小型系统的性能优点。因此，在存在不确定性的情况下设计复杂系统是很重要的。在这个项目中，PI计划为小尺度复杂系统的随机分析开发高效准确的算法。该项目旨在在复杂系统的随机分析相关的三个领域取得算法进展。第一个领域涉及核矩匹配技术的发展，以估计不确定输入的概率密度函数（pdf）。关键思想是估计pdf，以便优化输出统计信息。第二个领域涉及用于控制复杂系统的随机数学模型的数值分析算法的发展。第三个领域涉及开发用于复杂系统耦合分析的集成数据驱动随机算法。集成随机环境不仅可以用于复杂系统的鲁棒设计，还可以用于探索新型复杂系统的设计和开发。研究生和本科生，包括女性和代表性不足的学生，将在涉及算法、物理和工程的跨学科领域接受培训。