1202.0753 (Lorenzo Fagiano et al.)

Simulation of stochastic systems via polynomial chaos expansions and
convex optimization    [PDF]

Lorenzo Fagiano, Mustafa Khammash

Polynomial Chaos Expansions represent a powerful tool to simulate stochastic
models of dynamical systems. Yet, deriving the expansion's coefficients for
complex systems might require a significant and non-trivial manipulation of the
model, or the computation of large numbers of simulation runs, rendering the
approach too time consuming and impracticable for applications with more than a
handful of random variables. We introduce a novel computationally tractable
technique for computing the coefficients of polynomial chaos expansions. The
approach exploits a regularization technique with a particular choice of
weighting matrices, which allow to take into account the specific features of
Polynomial Chaos expansions. The method, completely based on convex
optimization, can be applied to problems with a large number of random
variables and uses a modest number of Monte Carlo simulations, while avoiding
model manipulations. Additional information on the stochastic process, when
available, can be also incorporated in the approach by means of convex
constraints. We show the effectiveness of the proposed technique in three
applications in diverse fields, including the analysis of a nonlinear electric
circuit, a chaotic model of organizational behavior, finally a chemical
oscillator.

View original: http://arxiv.org/abs/1202.0753