We develop a method to learn physical systems from data that employs
feedforward neural networks and whose predictions comply with the first and
second principles of thermodynamics. The method employs a minimum amount of
data by enforcing the metriplectic structure of dissipative Hamiltonian systems
in the form of the so-called General Equation for the Non-Equilibrium
Reversible-Irreversible Coupling, GENERIC [M. Grmela and H.C Oettinger (1997).
Dynamics and thermodynamics of complex fluids. I. Development of a general
formalism. Phys. Rev. E. 56 (6): 6620-6632]. The method does not need to
enforce any kind of balance equation, and thus no previous knowledge on the
nature of the system is needed. Conservation of energy and dissipation of
entropy in the prediction of previously unseen situations arise as a natural
by-product of the structure of the method. Examples of the performance of the
method are shown that include conservative as well as dissipative systems,
discrete as well as continuous ones.

利用前馈神经网络和热力学第一和第二定律，通过从数据中学习物理系统的方法，以及使用所谓的非平衡可逆耦合通用方程 (GENERIC) 的度规辛结构，可以最小化地使用数据。该方法不需要强制任何平衡方程式，因此不需要关于系统性质的任何先前知识。能量守恒和熵耗散是该方法结构的自然副产品。展示了该方法的性能示例，包括守恒和耗散系统以及离散和连续系统。