Contour location via entropy reduction leveraging multiple information sources

We introduce an algorithm to locate contours of functions that are expensive to evaluate. The problem of locating contours arise in many applications, including classification, constrained optimization, and analysis of performance of mechanical and dynamical systems (reliability, probability of failure, stability, etc.). Our algorithm locates contours using information from multiple sources, which are available in the form of relatively inexpensive, biased, and possibly noisy approximations to the original function. Considering multiple information sources can lead to significant cost savings. We also introduce the concept of contour entropy, a formal measure of uncertainty about the location of the zero contour of a function approximated by a statistical surrogate model.