Deep neural operators, such as DeepONets, have changed the paradigm in high-dimensional nonlinear regression from function regression to (differential) operator regression, paving the way for significant changes in computational engineering applications. Here, we investigate the use of DeepONets to infer flow fields around unseen airfoils with the aim of shape optimization, an important design problem in aerodynamics that typically taxes computational resources heavily. We present results which display little to no degradation in prediction accuracy, while reducing the online optimization cost by orders of magnitude. We consider NACA airfoils as a test case for our proposed approach, as their shape can be easily defined by the four-digit parametrization. We successfully optimize the constrained NACA four-digit problem with respect to maximizing the lift-to-drag ratio and validate all results by comparing them to a high-order CFD solver. We find that DeepONets have low generalization error, making them ideal for generating solutions of unseen shapes. Specifically, pressure, density, and velocity fields are accurately inferred at a fraction of a second, hence enabling the use of general objective functions beyond the maximization of the lift-to-drag ratio considered in the current work.
翻译:DeepONets等深神经操作器改变了高维非线性回归模式,从功能回归到(不同)操作器回归,为计算工程应用的重大变化铺平了道路。在这里,我们调查了DeepONets在以形状优化为目的的、在空气动力中的一个重要设计问题,通常对计算资源课税。我们展示了在预测准确性方面几乎没有到没有降解的结果,同时以数量级降低在线优化成本。我们认为,NACA Airfoils是测试我们拟议方法的一个实例,因为其形状很容易被四位数准位化所定义。我们成功地优化了NACA四位数限制的问题,在最大程度的升降至拉差比率方面,并验证了所有结果。我们发现,DeepONets具有低级的概括性错误,因此它们对于生成不可见形状的解决方案是理想的。具体地说,压力、密度和速度字段在第二小块上得到精确的推断,从而使得在最大程度的升升至最大程度之前能够使用一般目标功能。