Neural networks, especially the recent proposed neural operator models, are increasingly being used to find the solution operator of differential equations. Compared to traditional numerical solvers, they are much faster and more efficient in practical applications. However, one critical issue is that training neural operator models require large amount of ground truth data, which usually comes from the slow numerical solvers. In this paper, we propose a physics-guided data augmentation (PGDA) method to improve the accuracy and generalization of neural operator models. Training data is augmented naturally through the physical properties of differential equations such as linearity and translation. We demonstrate the advantage of PGDA on a variety of linear differential equations, showing that PGDA can improve the sample complexity and is robust to distributional shift.
翻译:神经网络,特别是最近提出的神经操作器模型,正越来越多地被用于寻找差异方程式的解决方案操作器。与传统的数字解算器相比,它们的实际应用速度更快、效率更高。然而,一个关键问题是,培训神经操作器模型需要大量的地面真相数据,这些数据通常来自缓慢的数字解算器。在本文件中,我们提出了物理学引导数据增强方法,以提高神经操作器模型的准确性和普遍性。培训数据通过线性和翻译等差异方程式的物理特性而自然增加。我们展示了PGDA在各种线性差异方程式方面的优势,表明PGDA可以提高样本的复杂性,并能够有力地进行分布式转换。