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.
Characterization of nanoparticle aggregates from observed scattered light leads to a highly complex inverse problem. Even the forward model is so complex that it prohibits the use of classical likelihood-based inference methods. In this study, we compare four so-called likelihood-free methods based on approximate Bayesian computation (ABC) that requires only numeric simulation of the forward model without the need of evaluating a likelihood. In particular, rejection, Markov chain Monte Carlo, population Monte Carlo, and adaptive population Monte Carlo (APMC) are compared in terms of accuracy. In the current model, we assume that the nanoparticle aggregates are mutually well separated and made up of particles of same size. Filippov's particle-cluster algorithm is used to generate aggregates, and discrete dipole approximation is used to estimate scattering behavior. It is found that the APMC algorithm is superior to others in terms of time and acceptance rates, although all algorithms produce similar posterior distributions. Using ABC techniques and utilizing unpolarized light experiments at 266 nm wavelength, characterization of soot aggregates is performed with less than 2 nm deviation in nanoparticle radius and 3-4 deviation in number of nanoparticles forming the monodisperse aggregates. Promising results are also observed for the polydisperse aggregate with log-normal particle size distribution.
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