Neural-Network-for-solving-PDE

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Neural-Network-for-solving-PDE

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Different methods of solving partial differential equations with neural networks

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# Neural-Network-for-solving-PDE
Different methods of solving partial differential equations with neural network  
# References:  
[1] M. Raissi, P. Perdikaris, and G. E. Karniadakis. Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics. https://linkinghub.elsevier.com/retrieve/pii/S0021999118307125  
  
[2] A. Al-Aradi, A. Correia, D. Naiff, G. Jardim and Y. Saporito, Solving Nonlinear and High-Dimensional Partial Differential Equations via Deep Learning, arXiv:1811.08782 [q-fin], Nov. 2018, Accessed: Oct. 01, 2021. [Online]. Available: http://arxiv.org/abs/1811.08782  
  
[3] J. Sirignano and K. Spiliopoulos, “DGM: A deep learning algorithm for solving partial differential equations,” Journal of Computational Physics. https://linkinghub.elsevier.com/retrieve/pii/S0021999118305527

[4] Zongyi Li, Nikola Kovachki, Kamyar Azizzadenesheli, Burigede Liu, Kaushik Bhattacharya, Andrew Stuart and Anima Anandkumar. Neural Operator: Graph Kernel Network for Partial Differential Equations. https://arxiv.org/abs/2003.03485

[5] V. Iakovlev, M. Heinonen, and H. Lähdesmäki, “Learning continuous-time PDEs from sparse data with graph neural networks,” arXiv:2006.08956 [cs, stat], Jan. 2021, Accessed: Oct. 11, 2021. [Online]. Available: http://arxiv.org/abs/2006.08956

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