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

Chengxi Zeng; Tilo Burghardt; Alberto M Gambaruto

doi:10.48550/arXiv.2402.08367

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 proceeding › Conference 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 language	English
Title of host publication	ICLR 2024
Subtitle of host publication	The Twelfth International Conference on Learning Representations
Number of pages	22
DOIs	https://doi.org/10.48550/arXiv.2402.08367
Publication status	E-pub ahead of print - 3 Mar 2024
Event	ICLR 2024: The Twelfth International Conference on Learning Representations - Messe Wien Exhibition and Congress Center, Vienna, Austria Duration: 7 May 2024 → 11 May 2024 https://iclr.cc/

Conference

Conference	ICLR 2024
Abbreviated title	ICLR 24
Country/Territory	Austria
City	Vienna
Period	7/05/24 → 11/05/24
Internet address	https://iclr.cc/

Bibliographical note

arXiv admin note: substantial text overlap with arXiv:2402.06955

Keywords

cs.LG

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Cite this

@inproceedings{4671fe69d0534b038dcb5e4dd08c8ece,

title = "RBF-PINN: Non-Fourier Positional Embedding in Physics-Informed Neural Networks",

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.",

keywords = "cs.LG",

author = "Chengxi Zeng and Tilo Burghardt and Gambaruto, {Alberto M}",

note = "arXiv admin note: substantial text overlap with arXiv:2402.06955; ICLR 2024 : The Twelfth International Conference on Learning Representations, ICLR 24 ; Conference date: 07-05-2024 Through 11-05-2024",

year = "2024",

month = mar,

day = "3",

doi = "10.48550/arXiv.2402.08367",

language = "English",

booktitle = "ICLR 2024",

url = "https://iclr.cc/",

}

TY - GEN

T1 - RBF-PINN

T2 - ICLR 2024

AU - Zeng, Chengxi

AU - Burghardt, Tilo

AU - Gambaruto, Alberto M

N1 - arXiv admin note: substantial text overlap with arXiv:2402.06955

PY - 2024/3/3

Y1 - 2024/3/3

N2 - 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.

AB - 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.

KW - cs.LG

U2 - 10.48550/arXiv.2402.08367

DO - 10.48550/arXiv.2402.08367

M3 - Conference Contribution (Conference Proceeding)

BT - ICLR 2024

Y2 - 7 May 2024 through 11 May 2024

ER -

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

Abstract

Conference

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Keywords

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