Use of BNNM for interference wave solutions of the gBS-like equation and comparison with PINNs
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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.
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References · 7
- 2017Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equationscited by 362
- 2017Hidden Physics Models: Machine Learning of Nonlinear Partial Differential Equationscited by 208
- 2017Machine Learning of Linear Differential Equations using Gaussian Processescited by 139
- 2017Numerical Gaussian Processes for Time-dependent and Non-linear Partial Differential Equationscited by 72
- 2016Inferring solutions of differential equations using noisy multi-fidelity datacited by 38
- 2021Physics-Informed Neural Network Method for Solving One-Dimensional Advection Equation Using PyTorchcited by 10
- 2021A Review of Physics-based Machine Learning in Civil Engineeringcited by 9
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