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

arXiv: https://arxiv.org/abs/2210.12154 · HTML: https://mlsanity.com/paper/2210.12154/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 18 references that are in the map.
- First posted on arXiv 7 Aug 2022.

## Builds on (most cited first, 7 of 7)

- [Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1711.10561/) (2017)
- [Hidden Physics Models: Machine Learning of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1708.00588/) (2017)
- [Machine Learning of Linear Differential Equations using Gaussian Processes](https://mlsanity.com/paper/1701.02440/) (2017)
- [Numerical Gaussian Processes for Time-dependent and Non-linear Partial Differential Equations](https://mlsanity.com/paper/1703.10230/) (2017)
- [Inferring solutions of differential equations using noisy multi-fidelity data](https://mlsanity.com/paper/1607.04805/) (2016)
- [Physics-Informed Neural Network Method for Solving One-Dimensional Advection Equation Using PyTorch](https://mlsanity.com/paper/2103.09662/) (2021)
- [A Review of Physics-based Machine Learning in Civil Engineering](https://mlsanity.com/paper/2110.04600/) (2021)

## Abstract (arXiv)

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.