Port-Hamiltonian Neural Networks for Learning Explicit Time-Dependent Dynamical Systems

Abstract

Accurately learning the temporal behavior of dynamical systems requires models with well-chosen learning biases. Recent innovations embed the Hamiltonian and Lagrangian formalisms into neural networks and demonstrate a significant improvement over other approaches in predicting trajectories of physical systems. These methods generally tackle autonomous systems that depend implicitly on time or systems for which a control signal is known apriori. Despite this success, many real world dynamical systems are non-autonomous, driven by time-dependent forces and experience energy dissipation. In this study, we address the challenge of learning from such non-autonomous systems by embedding the port-Hamiltonian formalism into neural networks, a versatile framework that can capture energy dissipation and time-dependent control forces. We show that the proposed \emph{port-Hamiltonian neural network} can efficiently learn the dynamics of nonlinear physical systems of practical interest and accurately recover the underlying stationary Hamiltonian, time-dependent force, and dissipative coefficient. A promising outcome of our network is its ability to learn and predict chaotic systems such as the Duffing equation, for which the trajectories are typically hard to learn.

arXiv comment[under review]

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• Physics-informed neural networks for quantum control
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• Pseudo-Hamiltonian Neural Networks with State-Dependent External Forces
• Gaussian Process Port-Hamiltonian Systems: Bayesian Learning with Physics Prior
• Structure-preserving Sparse Identification of Nonlinear Dynamics for Data-driven Modeling
• Noether Networks: Meta-Learning Useful Conserved Quantities
• Reversible and irreversible bracket-based dynamics for deep graph neural networks