Building surrogates with overcomplete bases in computer experiments with applications to bistable laser diodes

It is known that regular kriging models do not perform well in fitting and predicting computer experiments with complicated response surfaces. One such experiment arises in the dynamical system of bistable laser diodes for secure optical communications. The problem is challenging because the response surface is complicated, there are multiple solutions, and function evaluations are computationally expensive. Motivated by this problem, this article iteratively constructs surrogates for the complicated surface by using an overcomplete basis set. Application to the laser diodes problem shows that the proposed algorithms can solve the target problem by quickly capturing the trend of the response surface and efficiently guiding the search of desired solutions quickly. Performances and comparisons of the proposed algorithms and Gaussian process-based surrogate algorithms are presented to demonstrate the advantages of these methods.