Reduced Models and Uncertainty Quantification

Uncertainty quantification analyses the variability of system outputs with respect to process variations and thus represents a useful tool for robust design. Often statistics of a dynamical system’s outputs are quantities of interest. A sampling of the outputs requires many transient simulations. Due to the complexity of systems in nanoelectronics, methods of model order reduction (MOR) are applied for accelerating the uncertainty quantification. We consider coupled problems or multiphysics systems. We employ parametric MOR techniques to build parameter-dependent reduced-order models, which can be used for fast computations at all parameter samples. Samplingbased techniques like the Latin hypercube method, for example, or quadrature rules yield the parameter values. We apply this approach to an electrothermal coupled system. Furthermore, we illustrate a co-simulation technique with different quadrature grids for the subsystems. Now just some parts of a coupled problem are substituted by parametric MOR, if the others cannot be reduced efficiently. This method is applied to a circuit-electromagnetic coupled system.