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

复杂的系统，涉及多个学科之间的耦合相互作用，在微观和纳米尺度上是许多应用领域的基石，包括信息技术，能源和卫生部门。数据革命中的许多进步是由于小型化传感器及其网络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，小规模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。在小尺度下无法避免不确定性，例如物理/材料特性、几何形状、施加的信号等的变化。 这些不确定性可以显着影响复杂系统的性能，有时否定了小规模系统的性能优点。因此，在不确定性存在的情况下设计复杂系统是很重要的。在这个项目中，PI计划开发有效和准确的算法，用于小规模复杂系统的随机分析。该项目旨在在与复杂系统的随机分析相关的三个领域取得算法进步。第一个领域涉及核矩匹配技术的发展，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。第二个领域涉及复杂系统随机数学模型数值分析算法的开发。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。综合随机环境不仅将用于复杂系统的稳健设计，而且还将用于探索新型复杂系统的设计和开发，研究生和本科生，包括女生和人数不足的学生，将接受涉及算法、物理和工程的跨学科领域的培训。

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.