Abstract
Numerical models have to be used in most applications to characterize approximately the random fields describing the spatial fluctuation of material properties and estimate extremes and other functionals of materials responses. These models, referred to as finite dimensional (FD) models, are deterministic functions of the spatial coordinate and finite sets of random variables. Conditions are established under which the distributions of extremes and other functionals of material responses can be estimated from samples of material responses to FD material models. An one-dimensional stochastic transport equation is used to illustrate the construction and FD models and assess the accuracy of the extreme material response based on these models.
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