Learning Traveling Solitary Waves Using Separable Gaussian Neural Networks
Abstract
:1. Introduction
2. Methods
2.1. Architecture of SGNN for Traveling Waves
2.2. Physics-Informed Machine Learning
2.3. Training Scheme
3. Peakons in b-Family
3.1. Single Peakon
3.1.1. Camassa-Holm
3.1.2. Other Values of b
3.1.3. Interacting Peakons
3.1.4. Lefton Solutions
4. Peakons in ab-Family
5. 2D Compactons
6. Comparison and Discussion
7. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Figure | Training Loss | Validation Error | |
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8 | |||
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Network | Activation | Depth | Width | Loss | Trivial Solution? |
SGNN | GRBF | 1 | 40 | Yes | |
MLP | ReLu | 2 | 40 | Yes | |
ReLu | 4 | 40 | Yes | ||
ReLu | 6 | 40 | Yes | ||
ReLu | 8 | 20 | Yes | ||
sigmoid | 2 | 40 | Yes | ||
sigmoid | 4 | 40 | Yes | ||
sigmoid | 6 | 40 | Yes | ||
sigmoid | 8 | 20 | Yes | ||
tanh | 2 | 40 | Yes | ||
tanh | 4 | 40 | Yes | ||
tanh | 6 | 40 | Yes | ||
tanh | 8 | 20 | Yes |
Network | Activation | Depth | Width | Parameters | Loss | Trivial Solution? |
GRBF | 1 | 20 | 60 | No | ||
SGNN | GRBF | 1 | 40 | 120 | No | |
GRBF | 1 | 60 | 180 | No | ||
MLP | ReLu | 2 | 40 | 1640 | No | |
ReLu | 4 | 40 | 4840 | No | ||
ReLu | 6 | 40 | 8040 | No | ||
ReLu | 8 | 20 | 2820 | No | ||
sigmoid | 2 | 40 | 1640 | No | ||
sigmoid | 4 | 40 | 4840 | No | ||
sigmoid | 6 | 40 | 8040 | No | ||
sigmoid | 8 | 20 | 2820 | No | ||
tanh | 2 | 40 | 1640 | No | ||
tanh | 4 | 40 | 4840 | No | ||
tanh | 6 | 40 | 8040 | No | ||
tanh | 8 | 20 | 2820 | No |
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Xing, S.; Charalampidis, E.G. Learning Traveling Solitary Waves Using Separable Gaussian Neural Networks. Entropy 2024, 26, 396. https://doi.org/10.3390/e26050396
Xing S, Charalampidis EG. Learning Traveling Solitary Waves Using Separable Gaussian Neural Networks. Entropy. 2024; 26(5):396. https://doi.org/10.3390/e26050396
Chicago/Turabian StyleXing, Siyuan, and Efstathios G. Charalampidis. 2024. "Learning Traveling Solitary Waves Using Separable Gaussian Neural Networks" Entropy 26, no. 5: 396. https://doi.org/10.3390/e26050396