  Metriplectic systems are learned from data in a way that scales quadratically
in both the size of the state and the rank of the metriplectic data. Besides
being provably energy conserving and entropy stable, the proposed approach
comes with approximation results demonstrating its ability to accurately learn
metriplectic dynamics from data as well as an error estimate indicating its
potential for generalization to unseen timescales when approximation error is
low. Examples are provided which illustrate performance in the presence of both
full state information as well as when entropic variables are unknown,
confirming that the proposed approach exhibits superior accuracy and
scalability without compromising on model expressivity.
