High-Dimensional Variance-Based Adaptive Sampling for Prediction of Aerodynamic Flows Using Non-Intrusive Reduced Order Models

Abstract Non-intrusive reduced order modeling methods (ROMs) have been widely used as a computationally cheap method of modeling aerodynamic flows. A problem with the construction of these models is that a large number of samples are required to achieve global accuracy leading to a high cost of obtaining samples to create the ROMs. In this work, a novel adaptive sampling strategy is proposed that uses the uncertainty estimate of the high-dimensional prediction of the ROM as a sampling objective. The high-dimensional uncertainty estimate is obtained by performing Monte Carlo simulations to propagate the uncertainty of the low-dimensional space obtained using a multi-task Gaussian process model. The proposed algorithms are demonstrated on a two- and fourteen-dimensional aerodynamics modeling test case and compared to the performance of Halton sequences. The results of the two-dimensional case illustrate that the adaptive sampling strategies can achieve up to a 15% improvement over Halton sequences in terms of the mean relative error for the same number of samples. In the fourteen-dimensional test case, the adaptive sampling strategies achieve up to a 7.6% improvement over the Halton sequences at the same number of samples. All sampling strategies have comparable performance once the computational budget is exhausted, achieving a mean relative error of approximately 0.050 and 0.085 in the two- and fourteen-dimensional test cases, respectively. The adaptive sampling strategies can also better predict important features of the pressure distribution, such as shock waves and suction peaks.