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

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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.