RBF-PINN: Non-Fourier Positional Embedding in Physics-Informed Neural
  Networks
Chengxi Zeng Tilo Burghardt Alberto M Gambaruto
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.