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Neural networks, especially the recent proposed neural operator models, areincreasingly being used to find the solution operator of differentialequations. Compared to traditional numerical solvers, they are much faster andmore efficient in practical applications. However, one critical issue is thattraining neural operator models require large amount of ground truth data,which usually comes from the slow numerical solvers. In this paper, we proposea physics-guided data augmentation (PGDA) method to improve the accuracy andgeneralization of neural operator models. Training data is augmented naturallythrough the physical properties of differential equations such as linearity andtranslation. We demonstrate the advantage of PGDA on a variety of lineardifferential equations, showing that PGDA can improve the sample complexity andis robust to distributional shift.

Physics-guided Data Augmentation for Learning the Solution Operator of Linear Differential Equations