Dimension Bridging for 3D RANS with Neural Network Accelerated Gaussian Functional Regression

2026-08-27

AI Summary

研究使用神经网络加速的高斯函数回归来修正2D RANS模型，以准确预测3D RANS模型的空气动力学系数，减少高维计算需求并提高不确定性量化。

Abstract

In many computational science and engineering problems, repeatedly solving fully resolved physics-based models to design for a quantity of interest (QoI) can quickly become intractable, requiring the use of low-fidelity models to predict the same QoI but introduce errors where some features are neglected or are otherwise inaccurately resolved. We use Gaussian Functional Regression (GFR) to learn a correction to a 2D Reynolds-Averaged Navier-Stokes (RANS) model to predict the aerodynamic coefficients from a 3D RANS model. This model pair has a disparity in the governing physics from the reduced dimensionality, a previously unexplored application for GFR. Empirically, our results show that with a proper choice of low-dimensional (LD) model, the proposed kernel allows for the use of fewer high-dimensional (HD) evaluations to regress a response surface to the same level of accuracy as standard stationary kernels. Moreover, the new kernel provides more informative uncertainty quantification, which we show is advantageous when used to drive an adaptive sampling algorithm. Finally, we propose a novel neural network accelerated kernel, which we show offers predictions in good agreement while speeding up evaluations by millions of times in wall clock measurements, bringing the computational budget within the real-time regime.

Problem

• Gaussian Functional Regression
• Reynolds-Averaged Navier-Stokes
• dimensionality reduction
• computational efficiency
• uncertainty quantification

Innovation

• Gaussian Functional Regression
• Dimension Bridging
• Neural Network Acceleration
• Uncertainty Quantification