  Stochastic spectral methods have achieved great success in the uncertainty
quantification of many engineering problems, including electronic and photonic
integrated circuits influenced by fabrication process variations. Existing
techniques employ a generalized polynomial-chaos expansion, and they almost
always assume that all random parameters are mutually independent or Gaussian
correlated. However, this assumption is rarely true in real applications. How
to handle non-Gaussian correlated random parameters is a long-standing and
fundamental challenge. A main bottleneck is the lack of theory and
computational methods to perform a projection step in a correlated uncertain
parameter space. This paper presents an optimization-based approach to
automatically determinate the quadrature nodes and weights required in a
projection step, and develops an efficient stochastic collocation algorithm for
systems with non-Gaussian correlated parameters. We also provide some
theoretical proofs for the complexity and error bound of our proposed method.
Numerical experiments on synthetic, electronic and photonic integrated circuit
examples show the nearly exponential convergence rate and excellent efficiency
of our proposed approach. Many other challenging uncertainty-related problems
can be further solved based on this work.
