Gaussian process and design of experiments for surrogate modeling of optical properties of fractal aggregates

Abstract

A systematic approach based on the principles of supervised learning and design of experiments concepts is introduced to build a surrogate model for estimating the optical properties of fractal aggregates. The surrogate model is built on Gaussian process (GP) regression, and the input points for the GP regression are sampled with an adaptive sequential design algorithm. The covariance functions used are the squared exponential covariance function and the Matern covariance function both with Automatic Relevance Determination (ARD). The optical property considered is extinction efficiency of soot aggregates. The strengths and weaknesses of the proposed methodology are first tested with RDG-FA. Then, surrogate models are developed for the sampled points, for which the extinction efficiency is calculated by DDA. Four different uniformly gridded databases are also constructed for comparison. It is observed that the estimations based on the surrogate model designed with Matern covariance functions is superior to the estimations based on databases in terms of the accuracy of the estimations and the total number of input points they require. Finally, a preliminary surrogate model for S 11 is built to correct RDG-FA predictions with the aim of combining the speed of RDG-FA with the accuracy of DDA.

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“…Achieving an accurate surrogate model demands adequate input and output data. Given the cost of experimental work, training points are often generated through precise numerical simulations that consider several parameters for an observation, which can require considerable computation time [14,15]. Concerning the computational costs, recently, surrogate models was used to optimize the design of aerodynamic shapes, significantly reducing the computational effort required for each design evaluation [16].…”