GENERIC-FNO: Embedding Energy Conservation and Entropy Production into Fourier Neural Operators

GENERIC-FNO is a neural operator that embeds the metriplectic (GENERIC) degeneracy structure of nonequilibrium thermodynamics in function space. The method couples reversible, energy-conserving dynamics with irreversible, entropy-producing dynamics through degeneracy conditions, enabling simultaneous enforcement of multiple physical constraints. Prior structure-preserving neural operators enforce at most one conservation law or a Hamiltonian form, while thermodynamically consistent learning has been confined to finite-dimensional, graph, or particle systems. This work extends thermodynamic consistency to continuous function spaces for neural operators.