RBF-PINN: Non-Fourier Positional Embedding in Physics-Informed Neural Networks

2024/02/13 by Chengxi Zeng, Tilo Burghardt, Zeng, Chengxi +3 · 1 citation
Computer Science · #Computational Physics and Python Applications #FOS: Computer and information sciences #Machine Learning (cs.LG) #Neural Networks and Applications #Topic Modeling

paper · pdf · doi:10.48550/arxiv.2402.08367

openalex publication_date 2024/02/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

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.

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• Enforcing hidden physics in physics-informed neural networks

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