# A Generalized Metriplectic System via Free Energy and System~Identification via Bilevel Convex Optimization

arXiv: https://arxiv.org/abs/2410.06233 · HTML: https://mlsanity.com/paper/2410.06233/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Oct 2024.

## Built on by (most cited first, 3 of 3)

- [CHyLL: Learning Continuous Neural Representations of Hybrid Systems](https://mlsanity.com/paper/2512.10117/) (2025)
- [Embedding Hybrid Systems into Continuous Latent Vector Fields](https://mlsanity.com/paper/2606.10596/) (2026)
- [Learning Continuous Neural Representation of Stochastic Hybrid Systems](https://mlsanity.com/paper/2609.38893/) (2026)

## Abstract (arXiv)

This work generalizes the classical metriplectic formalism to model Hamiltonian systems with nonconservative dissipation. Classical metriplectic representations allow for the description of energy conservation and production of entropy via a suitable selection of an entropy function and a bilinear symmetric metric. By relaxing the Casimir invariance requirement of the entropy function, this paper shows that the generalized formalism induces the free energy analogous to thermodynamics. The monotonic change of free energy can serve as a more precise criterion than mechanical energy or entropy alone. This paper provides examples of the generalized metriplectic system in a 2-dimensional Hamiltonian system and SO(3). This paper also provides a bilevel convex optimization approach for the identification of the metriplectic system given measurements of the system.