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

Chengxi Zeng*, Tilo Burghardt*, Alberto M Gambaruto*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference Contribution (Conference Proceeding)

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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.
Original languageEnglish
Title of host publicationICLR 2024
Subtitle of host publicationThe Twelfth International Conference on Learning Representations
Number of pages22
DOIs
Publication statusE-pub ahead of print - 3 Mar 2024
EventICLR 2024: The Twelfth International Conference on Learning Representations - Messe Wien Exhibition and Congress Center, Vienna, Austria
Duration: 7 May 202411 May 2024
https://iclr.cc/

Conference

ConferenceICLR 2024
Abbreviated titleICLR 24
Country/TerritoryAustria
CityVienna
Period7/05/2411/05/24
Internet address

Bibliographical note

arXiv admin note: substantial text overlap with arXiv:2402.06955

Keywords

  • cs.LG

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