While many recent Physics-Informed Neural Networks (PINNs) variants have had considerable success in solving Partial Differential Equations, the empirical benefits of feature mapping drawn from the broader Neural Representations research have been largely overlooked. We highlight the limitations of widely used Fourier-based feature mapping in certain situations and suggest the use of the conditionally positive definite Radial Basis Function. The empirical findings demonstrate the effectiveness of our approach across a variety of forward and inverse problem cases. Our method can be seamlessly integrated into coordinate-based input neural networks and contribute to the wider field of PINNs research.

翻译：摘要：尽管近年来众多物理信息神经网络（PINN）变体在求解偏微分方程方面取得了显著成功，但源于更广泛神经表征研究的特征映射方法所得出的经验性优势在很大程度上被忽视了。我们揭示了广泛使用的基于傅里叶的特征映射在某些场景下的局限性，并提出了采用条件正定径向基函数的方案。实验结果表明，该方法在前向与逆向问题等多种案例中均具有有效性。本方法可无缝集成至基于坐标输入的神经网络中，并为PINN研究的更广领域作出贡献。