Contour location via entropy reduction leveraging multiple information sources
This work addresses the challenge of efficiently locating contours in expensive function evaluations, which is important for fields such as optimization and mechanical systems, though it appears incremental by building on existing surrogate modeling approaches.
The paper tackles the problem of locating contours of expensive-to-evaluate functions by introducing an algorithm that uses multiple cheaper, biased, and noisy information sources, achieving significant cost savings in applications like classification and reliability analysis.
We introduce an algorithm to locate contours of functions that are expensive to evaluate. The problem of locating contours arises in many applications, including classification, constrained optimization, and performance analysis 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. Our algorithm locates contours efficiently by maximizing the reduction of contour entropy per unit cost.