Constants of motion network reexamined

Area of Science:

• Dynamical Systems and Chaos Theory
• Computational Physics
• Machine Learning Applications

Background:

• Discovering constants of motion is crucial for understanding dynamical systems but requires advanced mathematical expertise.
• Neural network-based methods, like Constant of Motion Network (COMET), show promise but need further improvement for practical applications.

Purpose of the Study:

• To enhance the performance of existing neural network methods for discovering constants of motion.
• To develop a more lightweight and noise-robust approach compared to the current COMET method.

Main Methods:

• A novel neural network architecture utilizing singular-value-decomposition (SVD) was developed.
• A two-phase training algorithm was designed to optimize the network's performance.
• The proposed method was evaluated through extensive experiments.

Main Results:

• The new approach maintains COMET's ability to handle non-Hamiltonian systems and identify the number of constants of motion.
• Experimental results demonstrate that the proposed method is more lightweight and robust to noise than COMET.
• The SVD-based architecture and training algorithm significantly improve the efficiency and reliability of discovering constants of motion.

Conclusions:

• The proposed neural network architecture and training algorithm offer a superior alternative for discovering constants of motion.
• This advancement facilitates a deeper understanding of complex dynamical systems with improved computational efficiency and robustness.
• The method holds potential for broader applications in physics and engineering where dynamical system analysis is critical.