RBF-PINN: NON-FOURIER POSITIONAL EMBEDDING IN PHYSICS-INFORMED NEURAL NETWORKS

chengxi zeng, Tilo Burghardt, Alberto M Gambaruto

Keywords: PHYSICS-INFORMED NEURAL NETWORKS; PINNs; Feature Mapping; Positional Embedding

TL;DR: We proposed Radial Basis Function Positional Embedding for feature mapping in PINNs; it outperforms the commonly used Fourier-based features.

Abstract: 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.

Submission Number: 39