**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.

**Key Elements****:** Algorithm design and analysis of time/memory complexity, e.g. scalability of algorithms with respect to problem size, number of random dimensions; statistical analysis, e.g. generalized polynomial chaos theory; machine learning and data fitting techniques, e.g. extracting compact system models from exorbitantly large system measurements; C/C++ coding and linear algebra

**Research Issues**: 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

Example projects:

- VLSI circuits: Modeling the effect of channel length variation on massive integrated circuits involving upwards of few millions transistors.
- Electronic packaging: Modeling the effect of signal and power integrity due to variability in the geometric and physical dimensions of high-speed interconnects and power distribution networks.
- Computational Fluid Dynamics: Modeling the dynamic concentration of different species in complex fluidic systems
- Computational algorithms: We are currently invested in developing transformative algorithmic frameworks that can compress the near-exponential CPU time/memory costs exhibited by conventional polynomial chaos approaches with respect to number of random parameters. Current methods being investigated include parallelizable algorithms based on Schur’s complement method and waveform relaxation methods.
- Machine learning algorithms: Fast identification of stochastic models based on regression analysis is another key area of interest. We aim to further work on extend the capability of neural network based model to capture parametric uncertainty.
- High performance computing: Strategies to improve the poor scalability of polynomial chaos approaches based on decomposition of both physical and random space followed by parallel implementation of local polynomial chaos methodologies in each subdomain is currently being investigated. In future we will also focus on the scalability of such algorithms across different homogeneous and heterogeneous computing architectures will be investigated.

**Meeting Time****: **Friday, 3:00-5:00 ECE conference room

**Advisor****: **

- Sourajeet Roy (ECE), sjeetroy@engr.colostate.edu

**Laboratories Involved:**** **

- High Speed System Simulation Lab (CSU)
- Electromagnetics Lab (CSU)
- Computational Fluid Dynamics and Propulsion Lab (CSU)
- Integrated Microsystems Laboratory (McGill University)

**Disciplines Involved****:**

- Computer Engineering/Computer Science – CAD tools, complexity analysis of algorithms, high performance computing, machine learning, C/C++ programming
- Mathematics/Statistics: Random processes, Monte Carlo methods, high order quadrature and cubature techniques, generalized polynomial chaos theory
- Electrical Engineering – 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
- Mechanical Engineering – Computational fluid dynamics, high order finite volume methods, multispecies reacting fluid flows