  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.
