Complex-valued neural-operator-assisted soliton identification

Area of Science:

• Nonlinear dynamics
• Quantum physics
• Data-driven modeling

Background:

• Solitary states, or solitons, are crucial in Bose-Einstein condensates, nonlinear optics, and plasma physics.
• Accurate numerical determination of these states is essential for advancing these research areas.

Purpose of the Study:

• To propose a novel data-driven approach for identifying solitons.
• To leverage machine learning for solving differential equations in real-time.
• To enhance the study of solitary waves in nonlinear physical systems.

Main Methods:

• Utilizing a complex-valued neural operator (CNO) as a generalization of neural operators to the complex domain.
• Implementing an energy-restricted gradient optimization to constrain the search space for solitons.
• Applying the combined approach to quasi-one-dimensional Bose-Einstein condensates with varying nonlinearities.

Main Results:

• The CNO successfully maps initial states to final states, facilitating soliton identification.
• Energy-restricted optimization effectively guides the search for solitary states.
• Demonstrated efficacy on Bose-Einstein condensate models with homogeneous and inhomogeneous nonlinearities.

Conclusions:

• The proposed data-driven method offers an effective strategy for modeling and studying solitary waves.
• This approach provides a new avenue for analyzing nonlinear physical systems.
• Highlights the potential of machine learning in solving complex physics problems.