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.

翻译：我们基于端口-哈密顿形式体系，为复杂物理系统的机器学习开发了归纳偏置。为了确保所学物理规律中热力学原理（能量守恒、非负熵产生）得到满足，我们对端口-哈密顿形式体系进行了相应修改，从而构建出端口-度量辛形式体系。研究表明，所构建的网络能够分部件学习复杂系统的物理特性，从而减轻了该类系统的实验表征及后续学习过程带来的负担。然而，预测可在完整系统尺度上进行。文中通过实例展示了所提技术的性能表现。