发表机构
Oak Ridge National Laboratory（橡树岭国家实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对三维RANS与二维RANS的维度差异，提出神经网络加速的GFR核函数，可提升响应面回归精度、不确定性量化效果与评估速度，适配实时计算需求。
AI 中文摘要
在许多计算科学与工程问题中，为设计感兴趣量（QoI）反复求解全分辨率的基于物理的模型会很快变得难以处理，因此需要使用低保真模型来预测相同的QoI，但这类模型会因忽略某些特征或对特征的求解不准确而引入误差。我们使用高斯函数回归（GFR）学习对二维雷诺平均纳维-斯托克斯方程（RANS）模型的校正，以预测来自三维RANS模型的空气动力学系数。该模型对因降维存在控制物理的差异，这是GFR此前未探索过的应用场景。实验结果表明，通过恰当选择低维（LD）模型，所提出的核函数可使用更少的高维（HD）评估来回归响应面，达到与标准平稳核函数相同的精度水平。此外，新核函数能提供更具信息量的不确定性量化，我们证明这在驱动自适应采样算法时具有优势。最后，我们提出一种新颖的神经网络加速核函数，其预测结果吻合良好，且在墙钟时间测量中使评估速度提升了数百万倍，将计算预算控制在实时范围内。
英文摘要
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.
