mlsanityData to 14 Oct 2026

Efficiently Parameterized Neural Metriplectic Systems

arXiv 2405.16305 ↗First posted 25 May 2024cs.LGcited by 19

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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.

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

9 of 34 references.

References · 9

  1. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 9,122
  2. 2019Symplectic Recurrent Neural Networkscited by 150
  3. 2020Structure-preserving neural networkscited by 55
  4. 2021Machine learning structure preserving brackets for forecasting irreversible processescited by 52
  5. 2021GFINNs: GENERIC Formalism Informed Neural Networks for Deterministic and Stochastic Dynamical Systemscited by 49
  6. 2020Deep learning of thermodynamics-aware reduced-order models from datacited by 38
  7. 2021Structure-preserving Sparse Identification of Nonlinear Dynamics for Data-driven Modelingcited by 27
  8. 2023Reversible and irreversible bracket-based dynamics for deep graph neural networkscited by 26
  9. 2023Regular Time-series Generation using SGMcited by 23

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 1; 2025: 9; 2026: 9.

19 papers.

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  1. 2025Thermodynamically Consistent Latent Dynamics Identification for Parametric Systemscited by 8
  2. 2025Structure-Preserving Digital Twins via Conditional Neural Whitney Formscited by 8
  3. 2025Learning mechanical systems from real-world data using discrete forced Lagrangian dynamicscited by 7
  4. 2024SympGNNs: Symplectic Graph Neural Networks for identifiying high-dimensional Hamiltonian systems and node classificationcited by 4
  5. 2025SPIEDiff: robust learning of long-time macroscopic dynamics from short-time particle simulations with quantified epistemic uncertaintycited by 2
  6. 2025Rapid training of Hamiltonian graph networks using random featurescited by 2
  7. 2025Meta-learning Structure-Preserving Dynamicscited by 2
  8. 2026Metriplector: From Field Theory to Neural Architecturecited by 2
  9. 2025Moment Estimate and Variational Approach for Learning Generalized Diffusion with Non-gradient Structurescited by 1
  10. 2025Reduced-order modeling of Hamiltonian dynamics based on symplectic neural networkscited by 1
  11. 2026NN-OpInf: an operator inference approach using structure-preserving composable neural networkscited by 1
  12. 2026Structure-Aware Variational Learning of a Class of Generalized Diffusionscited by 1
7 more
  1. 2026Nonlinear GENERIC-Embedded Neural Networks (N-GENNs): Learning GENERIC dynamics with non-quadratic dissipation potentialscited by 1
  2. 2026GENERIC-FNO: Embedding Energy Conservation and Entropy Production into Fourier Neural Operatorscited by 1
  3. 2025Can Transformers overcome the lack of data in the simulation of history-dependent flows?cited by 0
  4. 2026Systematic Performance Assessment of Deep Material Networks for Multiscale Material Modelingcited by 0
  5. 2026CaLiSym: Learning Symplectic Dynamics of Real-World Systems through Structured Canonical Liftscited by 0
  6. 2026Structure-preserving uncertainty quantification for GENERIC dynamicscited by 0
  7. 2026Poisson-GENERIC Neural Operators: Exact Metriplectic Structure in Function Space via Casimir Entropiescited by 0