Solving the One-and-Two Dimensional STO Equations Based on the PINN Method

doi:10.13438/j.cnki.jdzk.2025.01.003

Abstract

Abstract: Physically informed neural networks (PINN) model are used to solve the one-and two-dimensional Sharam-Tasso-Olver equations.
The macroscopic equations and their initial margin conditions are used as physical information and transformed into the form of residuals,which are then used to construct a loss function to incorporate into the training process of the PINN model,and the Adam optimisation algorithm is used to achieve a high-precision solution.The numerical example results show that the loss function has high accuracy under a certain number of iterations,which verifies the reliability of the PINN model.

Key words: neural networks, physically informed neural network, Sharam-Tasso-Olver equation

WANG Jing, DAI Houping, DONG Yaru. Solving the One-and-Two Dimensional STO Equations Based on the PINN Method[J]. Journal of Jishou University(Natural Sciences Edition), 2025, 46(1): 18-24.

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