Details
| Originalsprache | Englisch |
|---|---|
| Aufsatznummer | 117518 |
| Seitenumfang | 37 |
| Fachzeitschrift | Computer Methods in Applied Mechanics and Engineering |
| Jahrgang | 433 |
| Frühes Online-Datum | 18 Nov. 2024 |
| Publikationsstatus | Veröffentlicht - 1 Jan. 2025 |
Abstract
AI for partial differential equations (PDEs) has garnered significant attention, particularly with the emergence of Physics-informed neural networks (PINNs). The recent advent of Kolmogorov–Arnold Network (KAN) indicates that there is potential to revisit and enhance the previously MLP-based PINNs. Compared to MLPs, KANs offer interpretability and require fewer parameters. PDEs can be described in various forms, such as strong form, energy form, and inverse form. While mathematically equivalent, these forms are not computationally equivalent, making the exploration of different PDE formulations significant in computational physics. Thus, we propose different PDE forms based on KAN instead of MLP, termed Kolmogorov–Arnold-Informed Neural Network (KINN) for solving forward and inverse problems. We systematically compare MLP and KAN in various numerical examples of PDEs, including multi-scale, singularity, stress concentration, nonlinear hyperelasticity, heterogeneous, and complex geometry problems. Our results demonstrate that KINN significantly outperforms MLP regarding accuracy and convergence speed for numerous PDEs in computational solid mechanics, except for the complex geometry problem. This highlights KINN's potential for more efficient and accurate PDE solutions in AI for PDEs.
ASJC Scopus Sachgebiete
- Ingenieurwesen (insg.)
- Numerische Mechanik
- Ingenieurwesen (insg.)
- Werkstoffmechanik
- Ingenieurwesen (insg.)
- Maschinenbau
- Physik und Astronomie (insg.)
- Allgemeine Physik und Astronomie
- Informatik (insg.)
- Angewandte Informatik
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in: Computer Methods in Applied Mechanics and Engineering, Jahrgang 433, 117518, 01.01.2025.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Kolmogorov–Arnold-Informed neural network
T2 - A physics-informed deep learning framework for solving forward and inverse problems based on Kolmogorov–Arnold Networks
AU - Wang, Yizheng
AU - Sun, Jia
AU - Bai, Jinshuai
AU - Anitescu, Cosmin
AU - Eshaghi, Mohammad Sadegh
AU - Zhuang, Xiaoying
AU - Rabczuk, Timon
AU - Liu, Yinghua
N1 - Publisher Copyright: © 2024
PY - 2025/1/1
Y1 - 2025/1/1
N2 - AI for partial differential equations (PDEs) has garnered significant attention, particularly with the emergence of Physics-informed neural networks (PINNs). The recent advent of Kolmogorov–Arnold Network (KAN) indicates that there is potential to revisit and enhance the previously MLP-based PINNs. Compared to MLPs, KANs offer interpretability and require fewer parameters. PDEs can be described in various forms, such as strong form, energy form, and inverse form. While mathematically equivalent, these forms are not computationally equivalent, making the exploration of different PDE formulations significant in computational physics. Thus, we propose different PDE forms based on KAN instead of MLP, termed Kolmogorov–Arnold-Informed Neural Network (KINN) for solving forward and inverse problems. We systematically compare MLP and KAN in various numerical examples of PDEs, including multi-scale, singularity, stress concentration, nonlinear hyperelasticity, heterogeneous, and complex geometry problems. Our results demonstrate that KINN significantly outperforms MLP regarding accuracy and convergence speed for numerous PDEs in computational solid mechanics, except for the complex geometry problem. This highlights KINN's potential for more efficient and accurate PDE solutions in AI for PDEs.
AB - AI for partial differential equations (PDEs) has garnered significant attention, particularly with the emergence of Physics-informed neural networks (PINNs). The recent advent of Kolmogorov–Arnold Network (KAN) indicates that there is potential to revisit and enhance the previously MLP-based PINNs. Compared to MLPs, KANs offer interpretability and require fewer parameters. PDEs can be described in various forms, such as strong form, energy form, and inverse form. While mathematically equivalent, these forms are not computationally equivalent, making the exploration of different PDE formulations significant in computational physics. Thus, we propose different PDE forms based on KAN instead of MLP, termed Kolmogorov–Arnold-Informed Neural Network (KINN) for solving forward and inverse problems. We systematically compare MLP and KAN in various numerical examples of PDEs, including multi-scale, singularity, stress concentration, nonlinear hyperelasticity, heterogeneous, and complex geometry problems. Our results demonstrate that KINN significantly outperforms MLP regarding accuracy and convergence speed for numerous PDEs in computational solid mechanics, except for the complex geometry problem. This highlights KINN's potential for more efficient and accurate PDE solutions in AI for PDEs.
KW - AI for PDEs
KW - AI for science
KW - Computational mechanics
KW - Kolmogorov–Arnold Networks
KW - PINNs
UR - http://www.scopus.com/inward/record.url?scp=85209232950&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2406.11045
DO - 10.48550/arXiv.2406.11045
M3 - Article
AN - SCOPUS:85209232950
VL - 433
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
SN - 0045-7825
M1 - 117518
ER -