Adaptive sampling physics-informed neural network method for high-order rogue waves and parameters discovery of the...

Area of Science:

• Physics
• Applied Mathematics
• Computational Science

Background:

• Rogue waves are significant phenomena with broad applications in fields like nonlinear optics and fluid dynamics.
• Traditional physics-informed neural networks (PINNs) struggle with high-dimensional partial differential equations (PDEs), particularly for high-order rogue waves, due to inefficient sampling of critical data regions.

Purpose of the Study:

• To introduce an adaptive sampling physics-informed neural network (ASPINN) method for improved prediction of rogue waves in high-dimensional PDEs.
• To address the limitations of standard PINNs in capturing the localized, sharp features of rogue waves.

Main Methods:

• Developed a novel adaptive search algorithm to ensure sufficient sampling of points within the sharp regions of rogue waves.
• Applied the ASPINN method to the (2+1)-dimensional CHKP equation as a test case.
• Investigated the data-driven inverse problem for the CHKP equation with varying noise levels to assess robustness.

Main Results:

• The ASPINN method significantly outperforms original PINNs in predicting the dynamical behaviors of high-order rogue waves for the CHKP equation.
• Prediction efficiency and accuracy were improved by up to four orders of magnitude.
• The ASPINN method demonstrated good robustness when applied to noisy data in inverse problem scenarios.

Conclusions:

• ASPINN effectively captures the complex dynamics of high-order rogue waves in high-dimensional PDEs.
• The adaptive sampling strategy is crucial for enhancing prediction performance and efficiency.
• ASPINN offers a robust and accurate solution for studying rogue wave phenomena and related inverse problems.