PINNs Based on the Burgers Equation
Abstract
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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References
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.
