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

• URL: http://arxiv.org/abs/2107.08024v1
• Date: Fri, 16 Jul 2021 17:31:54 GMT
• Title: Port-Hamiltonian Neural Networks for Learning Explicit Time-Dependent Dynamical Systems
• Authors: Shaan Desai, Marios Mattheakis, David Sondak, Pavlos Protopapas and Stephen Roberts
• Abstract summary: 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. We show that the proposed emphport-Hamiltonian neural network can efficiently learn the dynamics of nonlinear physical systems of practical interest.
• Score: 2.6084034060847894
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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