Poisson-GENERIC Neural Operators: Exact Metriplectic Structure in Function Space via Casimir Entropies
The paper develops a neural operator with an exact metriplectic structure for energy and entropy conservation. It achieves this by using augmented states where entropy becomes a Casimir of the evolution operator, eliminating projection steps. This structural approach ensures exact energy conservation and second law production, making it a robust surrogate model that adheres to physical laws even outside standard training data manifolds.