We develop inductive biases for the machine learning of complex physical
systems based on the port-Hamiltonian formalism. To satisfy by construction the
principles of thermodynamics in the learned physics (conservation of energy,
non-negative entropy production), we modify accordingly the port-Hamiltonian
formalism so as to achieve a port-metriplectic one. We show that the
constructed networks are able to learn the physics of complex systems by parts,
thus alleviating the burden associated to the experimental characterization and
posterior learning process of this kind of systems. Predictions can be done,
however, at the scale of the complete system. Examples are shown on the
performance of the proposed technique.

基于 Port-Hamiltonian 形式主义，我们开发了适用于复杂物理系统的机器学习归纳偏差，以构造满足热力学原则（能量守恒，非负熵产生）的学习物理。

端口多辛神经网络：物理系统的热力学知识驱动机器学习

Port-metriplectic neural networks: thermodynamics-informed machine learning of complex physical systems

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.

本文提出了一种基于端口哈密顿形式的神经网络模型用于学习非自主系统中的动态学，能够高效地恢复非线性物理系统的动力学，时间依赖力和耗散系数，并能够学习和预测混沌系统，如 Duffing 方程。