Port-Hamiltonian neural networks for learning explicit time-dependent dynamical systems.

Area of Science:

• Physics
• Machine Learning
• Dynamical Systems

Background:

• Learning temporal dynamics of physical systems requires effective model biases.
• Existing neural network approaches, based on Hamiltonian and Lagrangian formalisms, excel at autonomous systems but struggle with nonautonomous ones.
• Real-world systems often exhibit nonautonomous behavior, including time-dependent forces and energy dissipation, which are not well-captured by current models.

Purpose of the Study:

• To develop a neural network framework capable of learning dynamics from nonautonomous systems.
• To incorporate energy dissipation and time-dependent control forces into neural network models.
• To accurately recover system parameters like Hamiltonian, time-dependent forces, and dissipative coefficients.

Main Methods:

• Embedding the port-Hamiltonian formalism into neural networks.
• Developing a port-Hamiltonian neural network architecture.
• Testing the network on nonlinear physical systems, including chaotic ones like the Duffing equation.

Main Results:

• The port-Hamiltonian neural network efficiently learns the dynamics of nonlinear physical systems.
• The network accurately recovers the underlying stationary Hamiltonian, time-dependent force, and dissipative coefficient.
• The model demonstrates proficiency in learning and predicting chaotic system trajectories, such as those from the Duffing equation.

Conclusions:

• Port-Hamiltonian neural networks offer a versatile and effective approach for modeling nonautonomous dynamical systems.
• This framework advances the ability to learn complex physical behaviors, including dissipation and time-varying influences.
• The method shows significant promise for applications involving chaotic systems and real-world dynamics.