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Physics Informed by Deep Learning: Numerical Solutions of Modified Korteweg‐de Vries Equation

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  • Yuexing Bai
  • Temuer Chaolu
  • Sudao Bilige

Abstract

In this paper, with the aid of symbolic computation system Python and based on the deep neural network (DNN), automatic differentiation (AD), and limited‐memory Broyden‐Fletcher‐Goldfarb‐Shanno (L‐BFGS) optimization algorithms, we discussed the modified Korteweg‐de Vries (mkdv) equation to obtain numerical solutions. From the predicted solution and the expected solution, the resulting prediction error reaches 10−6. The method that we used in this paper had demonstrated the powerful mathematical and physical ability of deep learning to flexibly simulate the physical dynamic state represented by differential equations and also opens the way for us to understand more physical phenomena later.

Suggested Citation

  • Yuexing Bai & Temuer Chaolu & Sudao Bilige, 2021. "Physics Informed by Deep Learning: Numerical Solutions of Modified Korteweg‐de Vries Equation," Advances in Mathematical Physics, John Wiley & Sons, vol. 2021(1).
    • Handle: RePEc:wly:jnlamp:v:2021:y:2021:i:1:n:5569645
    DOI: 10.1155/2021/5569645
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    References listed on IDEAS

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    1. Helal, M.A. & Seadawy, A.R. & Zekry, M.H., 2014. "Stability analysis of solitary wave solutions for the fourth-order nonlinear Boussinesq water wave equation," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 1094-1103.
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