@article {678510, title = {Port-Hamiltonian Neural Networks for Learning Explicit Time-Dependent Dynamical Systems}, journal = {Phys Rev. E}, volume = {104}, year = {2021}, pages = {034312}, 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.}, url = {https://journals.aps.org/pre/abstract/10.1103/PhysRevE.104.034312}, author = {Shaan Desai and Marios Mattheakis and David Sondak and Pavlos Protopapas and Stephen Roberts} }