Use of BNNM for interference wave solutions of the gBS-like equation and comparison with PINNs

TL;DR

This paper introduces a bilinear neural network method (BNNM) for solving the gBS-like equation, demonstrating it is more accurate and faster than PINNs in modeling interference wave solutions.

Contribution

The work develops a novel BNNM approach for the gBS-like equation and compares its performance with PINNs, showing superior accuracy and efficiency.

Findings

BNNM accurately fits explicit solutions with zero error.

BNNM provides more accurate interference wave solutions than PINNs.

BNNM is computationally faster than PINNs.

Abstract

In this work, the generalized broken soliton-like (gBS-like) equation is derived through the generalized bilinear method. The neural network model, which can fit the explicit solution with zero error, is found. The interference wave solution of the gBS-like equation is obtained by using the bilinear neural network method (BNNM) and physical informed neural networks (PINNs). Interference waves are shown well via three-dimensional plots and density plots. Compared with PINNs, the bilinear neural network method is not only more accurate but also faster.