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Physics-guided multistage neural network: A physically guided network for step initial values and dispersive shock

Wen-Xuan Yuan¹, Rui Guo¹

¹Taiyuan University of Technology, School of Mathematics, Taiyuan 030024, China.

Physical Review. E

|February 7, 2025

Summary

This study introduces a physics-guided multistage neural network (PgMSNN) to accurately simulate complex dispersive shock waves (DSWs). The enhanced physics-informed neural network (PINN) model improves simulation accuracy and stability for nonlinear dynamics.

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Area of Science:

Nonlinear Dynamics
Computational Physics
Machine Learning

Background:

Dispersive shock waves (DSWs) are crucial in nonlinear dynamics but challenging to simulate.
Existing physics-informed neural networks (PINNs) require enhancement for complex dispersive phenomena.

Purpose of the Study:

To improve the simulation capabilities of PINNs for DSWs.
To develop an efficient and flexible tool for nonlinear dynamic systems.
To address the evolution of the generalized Gardner equation with step initial conditions.

Main Methods:

Integrated residual learning and a dispersion factor into PINNs.
Developed a Deep Runge-Kutta method for time-domain iteration.
Formulated a physics-guided multistage neural network (PgMSNN) with multistage training.

Main Results:

The PgMSNN model demonstrated enhanced accuracy and stability in simulating DSWs.
Successfully addressed forward problems, model stability, and parameter inversion.
Outperformed state-of-the-art neural network simulation methods.

Conclusions:

The PgMSNN model significantly improves PINN accuracy and stability for DSW phenomena.
Offers an efficient and flexible tool for simulating complex nonlinear systems.
Physics-guided deep learning strategies show great potential for complex physical problems.