论文标题
物理指导的数据增强，用于学习线性微分方程的解决方案操作员
Physics-guided Data Augmentation for Learning the Solution Operator of Linear Differential Equations
论文作者
论文摘要
神经网络，特别是最近提出的神经操作员模型，越来越多地用于找到微分方程的解决方案操作员。与传统的数值求解器相比，它们在实际应用中更快，更有效。但是，一个关键的问题是训练神经操作员模型需要大量的地面真相数据，这通常来自缓慢的数值求解器。在本文中，我们提出了一种物理引导的数据增强（PGDA）方法，以提高神经操作员模型的准确性和概括。通过线性和翻译等微分方程的物理特性自然增强了训练数据。我们证明了PGDA在多种线性微分方程上的优势，表明PGDA可以提高样品复杂性，并且对分布变化是可靠的。
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.
