Variable Fidelity Regression Using Low Fidelity Function Blackbox and Sparsification

Abstract

We consider construction of surrogate models based on variable fidelity samples generated by a high fidelity function an exact representation of some physical phenomenon and by a low fidelity function a coarse approximation of the exact representation. A surrogate model is constructed to replace the computationally expensive high fidelity function. For such tasks Gaussian processes are generally used. However, if the sample size reaches a few thousands points, a direct application of Gaussian process regression becomes impractical due to high computational costs. We propose two approaches to circumvent this difficulty. The first approach uses approximation of sample covariance matrices based on the Nystrom method. The second approach relies on the fact that engineers often can evaluate a low fidelity function on the fly at any point using some blackbox; thus each time calculating prediction of a high fidelity function at some point, we can update the surrogate model with the low fidelity function value at this point. So, we avoid issues related to the inversion of large covariance matrices -- as we can construct model using only a moderate low fidelity sample size. We applied developed methods to a real problem, dealing with an optimization of the shape of a rotating disk.