Thermodynamics-informed neural networks employ inductive biases for the enforcement of the first and second principles of thermodynamics. To construct these biases, a metriplectic evolution of the system is assumed. This provides excellent results, when compared to uninformed, black box networks. While the degree of accuracy can be increased in one or two orders of magnitude, in the case of graph networks, this requires assembling global Poisson and dissipation matrices, which breaks the local structure of such networks. In order to avoid this drawback, a local version of the metriplectic biases has been developed in this work, which avoids the aforementioned matrix assembly, thus preserving the node-by-node structure of the graph networks. We apply this framework for examples in the fields of solid and fluid mechanics. Our approach demonstrates significant computational efficiency and strong generalization capabilities, accurately making inferences on examples significantly different from those encountered during training.

这项研究通过引入感知力偏差，同时套用热力学第一和第二原理，提高神经网络的准确性，尤其是在涉及到图网络时，通过开发一种本地化版本的感知力偏差，避免了全局Poisson和耗散矩阵的拼装，从而保存了图网络的节点结构，并在固体力学和流体力学领域进行了应用，展示出显著的计算效率和高强度的泛化能力。

基于热力学局部启发的图神经网络