Uncertainties can cause significant performance degradations and functional failures in numerous engineering systems. Examples include (but are not limited to) nanoscale devices and systems with fabrication process variations, robot control without full knowledge of design and/or environmental parameters, energy systems with weather-dependent renewable energy sources, and magnetic resonance imaging (MRI) with incomplete and noisy scanning data. Modeling, controlling and optimizing these problems are generally data-intensive: one has to generate and analyze a huge amount of costly data in a parameter space. This often leads to the notorious curse of dimensionality: the complexity grows extremely fast with the number of uncertainty or/and design parameters.

This talk introduces some of our fast non-Monte-Carlo techniques and software for estimating the uncertain performance of engineering systems. The main application is variability analysis of nanoscale IC, MEMS and integrated photonics. Extended applications include energy systems and MRI. These techniques can accelerate a lot of uncertainty-aware optimization, control and data inference tasks (e.g., yield optimization of silicon chips, robust control of robots and power systems, electrical property tomography using MRI data). The first part will present some fast algorithms to simulate nonlinear dynamic systems influenced by a small number of uncertain parameters. The second part will present some high-dimensional algorithms to predict the performance uncertainties of an engineering system influenced by many random parameters.