Modern composite structures have a wide spread in their failure stress.  Advanced multiphysics codes can have a wide range of predicted behavior for nominally the same inputs.  How do we certify the design of such structures or the accuracy of such codes?

The quantification of uncertainties in engineering design has garnered som interest in recent years.  The most accurate method of quantifying the spread of outcomes of an experiment is the Monte Carlo approach. However, the cost of Monte Carlo simulations has caused most researchers to use some form of reliability analysis (no pun intended).  Such approaches reduce the number of tests that are needed to quantify the behavior of a structure.  However, some probability distribution function has to be assumed for the input parameters.  An alternative is to solve a stochastic set of differential equations - often using the Stochastic finite element method.

A recent paper by Lucas, Owhadi, Ortiz takes a slightly different tack.  They claim to provide tight upper bounds on the uncertainty through concentration of measure inequalities.  Does anyone have a good idea of what these are and could they explain it to a lay audience?  I'll also attempt to explain this idea as I learn more about it.

Links will be added as I learn about them. 

-- Biswajit