A Dimension-Augmented Physics-Informed Neural Network (DaPINN) with High Level Accuracy and Efficiency
This improves PINNs for scientific and commercial applications by enhancing accuracy and efficiency, though it is incremental as it builds on existing PINN methods.
The paper tackles the low accuracy and efficiency of Physics-Informed Neural Networks (PINNs) for solving partial differential equations by proposing a dimension-augmented PINN (DaPINN), which reduces error by 1-2 orders of magnitude compared to PINN in most experiments.
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.