# Efficiently Parameterized Neural Metriplectic Systems

arXiv: https://arxiv.org/abs/2405.16305 · HTML: https://mlsanity.com/paper/2405.16305/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 34 references that are in the map.
- First posted on arXiv 25 May 2024.

## Builds on (most cited first, 9 of 9)

- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Symplectic Recurrent Neural Networks](https://mlsanity.com/paper/1909.13334/) (2019)
- [Structure-preserving neural networks](https://mlsanity.com/paper/2004.04653/) (2020)
- [Machine learning structure preserving brackets for forecasting irreversible processes](https://mlsanity.com/paper/2106.12619/) (2021)
- [GFINNs: GENERIC Formalism Informed Neural Networks for Deterministic and Stochastic Dynamical Systems](https://mlsanity.com/paper/2109.00092/) (2021)
- [Deep learning of thermodynamics-aware reduced-order models from data](https://mlsanity.com/paper/2007.03758/) (2020)
- [Structure-preserving Sparse Identification of Nonlinear Dynamics for Data-driven Modeling](https://mlsanity.com/paper/2109.05364/) (2021)
- [Reversible and irreversible bracket-based dynamics for deep graph neural networks](https://mlsanity.com/paper/2305.15616/) (2023)
- [Regular Time-series Generation using SGM](https://mlsanity.com/paper/2301.08518/) (2023)

## Built on by (most cited first, 19 of 19)

- [Thermodynamically Consistent Latent Dynamics Identification for Parametric Systems](https://mlsanity.com/paper/2506.08475/) (2025)
- [Structure-Preserving Digital Twins via Conditional Neural Whitney Forms](https://mlsanity.com/paper/2508.06981/) (2025)
- [Learning mechanical systems from real-world data using discrete forced Lagrangian dynamics](https://mlsanity.com/paper/2505.20370/) (2025)
- [SympGNNs: Symplectic Graph Neural Networks for identifiying high-dimensional Hamiltonian systems and node classification](https://mlsanity.com/paper/2408.16698/) (2024)
- [SPIEDiff: robust learning of long-time macroscopic dynamics from short-time particle simulations with quantified epistemic uncertainty](https://mlsanity.com/paper/2505.13501/) (2025)
- [Rapid training of Hamiltonian graph networks using random features](https://mlsanity.com/paper/2506.06558/) (2025)
- [Meta-learning Structure-Preserving Dynamics](https://mlsanity.com/paper/2508.11205/) (2025)
- [Metriplector: From Field Theory to Neural Architecture](https://mlsanity.com/paper/2603.29496/) (2026)
- [Moment Estimate and Variational Approach for Learning Generalized Diffusion with Non-gradient Structures](https://mlsanity.com/paper/2508.01854/) (2025)
- [Reduced-order modeling of Hamiltonian dynamics based on symplectic neural networks](https://mlsanity.com/paper/2508.11911/) (2025)
- [NN-OpInf: an operator inference approach using structure-preserving composable neural networks](https://mlsanity.com/paper/2603.08488/) (2026)
- [Structure-Aware Variational Learning of a Class of Generalized Diffusions](https://mlsanity.com/paper/2604.20188/) (2026)
- [Nonlinear GENERIC-Embedded Neural Networks (N-GENNs): Learning GENERIC dynamics with non-quadratic dissipation potentials](https://mlsanity.com/paper/2605.09058/) (2026)
- [GENERIC-FNO: Embedding Energy Conservation and Entropy Production into Fourier Neural Operators](https://mlsanity.com/paper/2606.08343/) (2026)
- [Can Transformers overcome the lack of data in the simulation of history-dependent flows?](https://mlsanity.com/paper/2512.16305/) (2025)
- [Systematic Performance Assessment of Deep Material Networks for Multiscale Material Modeling](https://mlsanity.com/paper/2602.07192/) (2026)
- [CaLiSym: Learning Symplectic Dynamics of Real-World Systems through Structured Canonical Lifts](https://mlsanity.com/paper/2607.06824/) (2026)
- [Structure-preserving uncertainty quantification for GENERIC dynamics](https://mlsanity.com/paper/2608.12624/) (2026)
- [Poisson-GENERIC Neural Operators: Exact Metriplectic Structure in Function Space via Casimir Entropies](https://mlsanity.com/paper/2610.05570/) (2026)

## Abstract (arXiv)

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.