# Variational Analysis and Reliability Modeling Algorithms (VARMA)

## Goals

With the ever increasing complexity of engineering systems, parametric uncertainty arising due to manufacturing process variations, variations in operating environment and from simplifying assumptions made during the design process have become crucial in determining the performance, reliability, and life-span of such systems. Modeling the propagation of this uncertainty from the system parameters to the system behavior requires a completely novel and stochastic approach towards characterization of engineering systems. Thus, the objective of this program is to develop new cutting edge mathematical knowledge and computational tools for rapid and accurate uncertainty quantification and reliability analysis of complex engineering systems.

## Issues Involved or Addressed

Time/memory scalability of conventional polynomial chaos algorithms with respect to number of random parameters; global sensitivity analysis for assessing the relative impact of multiple random parameters to overall system statistics; developing parallelizable polynomial chaos techniques for rapid uncertainty quantification of electrical circuits, electromagnetic systems, microwave and RF circuits, mechanical systems such as fluidic and combustion systems; performance optimization of engineering systems in the presence of rampant parametric uncertainty

## Methods and Technologies

## Academic Majors of Interest

## Preferred Interests and Preparation

CAD tools, complexity analysis of algorithms, high performance computing, machine learning, C/C++ programming, random processes, Monte Carlo methods, high order quadrature and cubature techniques, generalized polynomial chaos theory, integrated circuit design, computational electromagnetics, microwave and RF circuit simulation, compressed sensing and regression analysis, model order reduction, linear/nonlinear system identification and behavioral modeling, computational fluid dynamics, high order finite volume methods, multispecies reacting fluid flows