PINNs Based on the Burgers Equation

Autores

  • Vitória Biesek
  • Anderson B. Modena
  • Pedro H.A. Konzen

Resumo

A Physics-informed neural network (PINN) is a deep learning framework for solving partial differential equations (PDEs). Deep learning is a field of machine learning by multiple levels of composition [1]. Introduced in the paper [2], the PINNs have since gain attention by its simplicity and potential efficiency as a general purpose solver for PDEs (see, for instance, [3]). [...]

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Biografia do Autor

Vitória Biesek

IME, UFRGS, RS

Anderson B. Modena

IME, UFRGS, RS

Pedro H.A. Konzen

IME, UFRGS, RS

Referências

I. Goodfellow, Y. Bengio, and A. Courville. Deep Learning. London: Massachusetts Institute of Technology, 2014. isbn: 9780262035613.

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”. In: Journal of Computational Physics 378 (2019), pp. 686–707. doi: 10.1016/j.jcp.2018.10.045.

F.F. Mata, A. Gijón, M. Molina-Solana, and J. Gómez-Romero. “Physics-informed neural networks for data-driven simulation: Advantages, limitations, and opportunities”. In: Physica A: Statistical Mechanics and its Applications 610 (2023), p. 128415. issn: 0378-4371. doi: 10.1016/j.physa.2022.128415.

P.H.A. Konzen, F.S. Azevedo, E. Sauter, and P.R.A. Zingano. “Numerical Simulations with the Galerkin Least Squares Finite Element Method for the Burgers’ Equation on the Real Line”. In: Tendências em Matemática Aplicada e Computacional 18.2 (2017), pp. 287–304. doi: 10.5540/tema.2017.018.02.0287.

S. Haykin. Neural Networks: A Comprehensive Foundation. Delhi: Pearson, 2005. isbn: 9788177588521.

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Publicado

2023-12-18

Edição

Seção

Resumos