  In this paper we present a deep learning method to predict the temporal
evolution of dissipative dynamic systems. We propose using both geometric and
thermodynamic inductive biases to improve accuracy and generalization of the
resulting integration scheme. The first is achieved with Graph Neural Networks,
which induces a non-Euclidean geometrical prior with permutation invariant node
and edge update functions. The second bias is forced by learning the GENERIC
structure of the problem, an extension of the Hamiltonian formalism, to model
more general non-conservative dynamics. Several examples are provided in both
Eulerian and Lagrangian description in the context of fluid and solid mechanics
respectively, achieving relative mean errors of less than 3% in all the tested
examples. Two ablation studies are provided based on recent works in both
physics-informed and geometric deep learning.
