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

Physics-informed neural networks (PINNs) have been widely applied in different fields due to their effectiveness solving partial differential equations (PDEs). However, the accuracy and efficiency of PINNs need be considerably improved for scientific commercial purposes. To address this issue, we systematically propose a novel dimension-augmented physics-informed network (DaPINN), which simultaneously significantly improves base PINN. In DaPINN model, manipulate dimensionality input by inserting additional sample features then incorporate expanded into loss function. Moreover, verify power series augmentation, Fourier augmentation replica both forward backward problems. most experiments, error is 1 ∼2 orders magnitude lower than that The results show outperforms original PINN terms with reduced dependence on number points. We also discuss computational complexity DaPINN, its size implications, other implementations compatibility DaPINN's methods residual-based adaptive refinement (RAR), self-adaptive (SA-PINNs) gradient-enhanced (gPINNs).