Physics-enhanced neural networks learn order and chaos

Area of Science:

• Computational physics
• Machine learning
• Dynamical systems

Background:

• Artificial neural networks (ANNs) are powerful function approximators capable of forecasting dynamical systems.
• However, ANNs may require an impractically large number of neurons for chaotic or complex dynamics.
• Efficiently learning phase space orbits in nonlinear systems transitioning to chaos remains a challenge.

Purpose of the Study:

• To introduce and demonstrate Hamiltonian neural networks (HNNs) for efficient learning of phase space orbits.
• To showcase HNNs' capability in handling nonlinear systems, including those exhibiting chaotic behavior.
• To elucidate the forecasting mechanisms of HNNs through introspection.

Main Methods:

• Development and application of neural networks incorporating Hamiltonian dynamics principles.
• Utilizing HNNs to learn phase space orbits in benchmark dynamical systems.
• Testing HNNs on the Hénon-Heiles potential and nonperturbative dynamical billiards.

Main Results:

• Demonstrated efficient learning of phase space orbits by HNNs, even in systems transitioning from order to chaos.
• Successfully applied HNNs to established dynamics benchmarks, including the Hénon-Heiles potential.
• Validated HNNs' performance on nonperturbative dynamical billiards, showcasing their versatility.

Conclusions:

• Hamiltonian neural networks offer an efficient method for learning complex dynamics and phase space orbits.
• HNNs provide a promising approach to overcome the limitations of traditional ANNs in forecasting chaotic systems.
• The introspective analysis of HNNs aids in understanding their forecasting capabilities for nonlinear dynamics.