Adaptive Sampling for Non-intrusive Reduced Order Models Using Multi-task Variance

Non-intrusive reduced order modeling methods (ROMs) have become increasingly popular for science and engineering applications such as predicting the field-based solutions for aerodynamic flows. A large sample size is, however, required to train the models for global accuracy. In this paper, a novel adaptive sampling strategy is introduced for these models that uses field-based uncertainty as a sampling metric. The strategy uses Monte Carlo simulations to propagate the uncertainty in the prediction of the latent space of the ROM obtained using a multi-task Gaussian process to the high-dimensional solution of the ROM. The high-dimensional uncertainty is used to discover new sampling locations to improve the global accuracy of the ROM with fewer samples. The performance of the proposed method is demonstrated on the environment model function and compared to one-shot sampling strategies. The results indicate that the proposed adaptive sampling strategies can reduce the mean relative error of the ROM to the order of 8×10^-4 which is a 20% and 27% improvement over the Latin hypercube and Halton sequence sampling strategies, respectively at the same number of samples.