https://doi.org/10.1140/epjp/s13360-022-03078-8
Regular Article
Solving Benjamin–Ono equation via gradient balanced PINNs approach
School of Mathematical Sciences, Dalian University of Technology, 116024, Dalian, People’s Republic of China
Received:
2
March
2022
Accepted:
15
July
2022
Published online:
26
July
2022
Soliton solution of Benjamin–Ono (BO) equation has considerable applications in physical field. In this paper, we utilize the Physics-informed neural networks (PINNs) to solve the soliton solution of the BO equation firstly. However, we discern that the imbalance phenomenon of back-propagated gradients occurs between residual loss and initial values or boundary conditions, which leads to the loss function failing to converge well during model training. In order to overcome the faultiness, we introduce self-adaptive parameters into the loss function in PINNs to balance the effect between different terms in original loss function, namely Gradient Balanced PINNs approach. By comparing the performance of solving BO equation, numerical results showed that the prediction accuracy of improved method has improved significantly and absolute error is reduced by order of magnitude. Finally, relevant results have been exhibited in tables and diagrams, dynamical behaviors and error analysis by employing two methods are revealed in detail.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2022
