  Physics-informed neural networks (PINNs) have been widely applied in
different fields due to their effectiveness in solving partial differential
equations (PDEs). However, the accuracy and efficiency of PINNs need to be
considerably improved for scientific and commercial use. To address this issue,
we systematically propose a novel dimension-augmented physics-informed neural
network (DaPINN), which simultaneously and significantly improves the accuracy
and efficiency of the PINN. In the DaPINN model, we introduce inductive bias in
the neural network to enhance network generalizability by adding a special
regularization term to the loss function. Furthermore, we manipulate the
network input dimension by inserting additional sample features and
incorporating the expanded dimensionality in the loss function. Moreover, we
verify the effectiveness of power series augmentation, Fourier series
augmentation and replica augmentation, in both forward and backward problems.
In most experiments, the error of DaPINN is 1$\sim$2 orders of magnitude lower
than that of PINN. The results show that the DaPINN outperforms the original
PINN in terms of both accuracy and efficiency with a reduced dependence on the
number of sample points. We also discuss the complexity of the DaPINN and its
compatibility with other methods.
