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Physics-informed neural networks (PINNs) have been widely applied indifferent fields due to their effectiveness in solving partial differentialequations (PDEs). However, the accuracy and efficiency of PINNs need to beconsiderably improved for scientific and commercial use. To address this issue,we systematically propose a novel dimension-augmented physics-informed neuralnetwork (DaPINN), which simultaneously and significantly improves the accuracyand efficiency of the PINN. In the DaPINN model, we introduce inductive bias inthe neural network to enhance network generalizability by adding a specialregularization term to the loss function. Furthermore, we manipulate thenetwork input dimension by inserting additional sample features andincorporating the expanded dimensionality in the loss function. Moreover, weverify the effectiveness of power series augmentation, Fourier seriesaugmentation and replica augmentation, in both forward and backward problems.In most experiments, the error of DaPINN is 1$\sim$2 orders of magnitude lowerthan that of PINN. The results show that the DaPINN outperforms the originalPINN in terms of both accuracy and efficiency with a reduced dependence on thenumber of sample points. We also discuss the complexity of the DaPINN and itscompatibility with other methods.

A Dimension-Augmented Physics-Informed Neural Network (DaPINN) with High Level Accuracy and Efficiency