We consider the problem of using SciML to predict solutions of high Mach fluid flows over irregular geometries. In this setting, data is limited, and so it is desirable for models to perform well in the low-data setting. We show that Neural Basis Functions (NBF), which learns a basis of behavior modes from the data and then uses this basis to make predictions, is more effective than a basis-unaware baseline model. In addition, we identify continuing challenges in the space of predicting solutions for this type of problem.

翻译：我们考虑利用科学机器学习方法预测不规则几何体上的高马赫流体流动解的问题。在此设定下，数据较为有限，因此模型在低数据场景下具有良好的性能十分重要。研究表明，神经基函数方法从数据中学习行为模态基函数，并利用该基函数进行预测，其效果优于未建立基函数的基准模型。此外，我们指出了在预测此类问题解时仍存在的持续挑战。