用可观测变量建模耗散系统，确保熵不减且参数少
Variational Neural Networks for Observable Thermodynamics (V-NOTS)
- 基于热力学拉格朗日构建神经网络，只依赖可观测变量
- 仅用少量数据点和参数即可准确描述相空间演化
- 适合缺乏完整状态信息的物理系统建模
近期研究聚焦于基于数据计算物理系统演化。此类方法利用相空间中过去轨迹的数据点，重构运动方程并预测未观测到的未来解。然而，许多情况下可用数据并不对应系统相空间的定义变量。本文关注耗散动力系统这一重要情形：其相空间包含坐标、动量与熵，但动量和熵通常无法直接观测。为解决此问题，我们提出一种仅依赖可观测变量的数据驱动计算框架，基于热力学拉格朗日构造新型神经网络，确保系统满足热力学规律且熵永不减少。实验表明，该网络可在有限数据点和较少参数条件下，高效描述相空间演化。
原文摘要 · Abstract (English)
Much attention has recently been devoted to data-based computing of evolution of physical systems. In such approaches, information about data points from past trajectories in phase space is used to reconstruct the equations of motion and to predict future solutions that have not been observed before. However, in many cases, the available data does not correspond to the variables that define the system's phase space. We focus our attention on the important example of dissipative dynamical systems. In that case, the phase space consists of coordinates, momenta and entropies; however, the momenta and entropies cannot, in general, be observed directly. To address this difficulty, we develop an efficient data-based computing framework based exclusively on observable variables, by constructing a novel approach based on the thermodynamic Lagrangian, and constructing neural networks that respect the thermodynamics and guarantees the non-decreasing entropy evolution. We show that our network can provide an efficient description of phase space evolution based on a limited number of data points and a relatively small number of parameters in the system.
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