论文标题
具有结构的神经网络
Structure-preserving neural networks
论文作者
论文摘要
我们开发了一种从采用前馈神经网络的数据中学习物理系统的方法，其预测符合热力学的第一和第二原理。该方法通过以所谓的一般方程式的形式实施耗散性汉密尔顿系统的宫颈结构来采用最少的数据，用于非平衡可逆 - 可逆的可逆耦合，通用的通用耦合[M. Grmela和H.C Oettinger（1997）。复杂流体的动力学和热力学。一般形式主义的发展。物理。 Rev. E. 56（6）：6620-6632]。该方法不需要执行任何平衡方程，因此不需要以前关于系统性质的知识。在预测以前看不见的情况下的能量保存和熵的耗散是该方法结构的自然副产品。该方法的性能的示例显示，包括保守和耗散系统，离散和连续的系统。
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.
