We present a numerical technique to visualize covariance and cross-covariance fields of a stochastic simulation. The method is local in the sense that it demonstrates the covariance structure of the solution at a point with its neighboring locations. When coupled with an efficient stochastic simulation solver, our framework allows one to effectively concurrently visualize both the mean and (cross-)covariance information for two-dimensional (spatial) simulation results. Most importantly, the visualization provides the scientist a means to identify interesting correlation structure of the solution field. The mathematical setup is discussed, along with several examples to demonstrate the efficacy of this approach.
The approach in REF suggests a numerical technique for visualizing covariance and crosscovariance fields of 2-dimensional results of stochastic simulations.
VISUALIZATION OF COVARIANCE AND CROSS-COVARIANCE FIELDS
International Journal for Uncertainty Quantification
Mathematics