mlsanityData to 7 Oct 2026

Deep learning of thermodynamics-aware reduced-order models from data

arXiv 2007.03758 ↗First posted 3 Jul 2020cs.CE cs.LG stat.MLcited by 38

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Abstract (arXiv)

We present an algorithm to learn the relevant latent variables of a large-scale discretized physical system and predict its time evolution using thermodynamically-consistent deep neural networks. Our method relies on sparse autoencoders, which reduce the dimensionality of the full order model to a set of sparse latent variables with no prior knowledge of the coded space dimensionality. Then, a second neural network is trained to learn the metriplectic structure of those reduced physical variables and predict its time evolution with a so-called structure-preserving neural network. This data-based integrator is guaranteed to conserve the total energy of the system and the entropy inequality, and can be applied to both conservative and dissipative systems. The integrated paths can then be decoded to the original full-dimensional manifold and be compared to the ground truth solution. This method is tested with two examples applied to fluid and solid mechanics.

Key facts. Cited by 38 papers in the map (data through 7 Oct 2026). First posted on arXiv 3 Jul 2020.

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Citing papers per year: 2021: 7; 2022: 7; 2023: 3; 2024: 9; 2025: 7; 2026: 5.

38 papers.

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  1. 2021GFINNs: GENERIC Formalism Informed Neural Networks for Deterministic and Stochastic Dynamical Systemscited by 48
  2. 2023A graph convolutional autoencoder approach to model order reduction for parametrized PDEscited by 44
  3. 2022Thermodynamics-informed graph neural networkscited by 31
  4. 2021The mixed deep energy method for resolving concentration features in finite strain hyperelasticitycited by 28
  5. 2024tLaSDI: Thermodynamics-informed latent space dynamics identificationcited by 23
  6. 2022A deep learning energy method for hyperelasticity and viscoelasticitycited by 20
  7. 2021Multiscale modeling of inelastic materials with Thermodynamics-based Artificial Neural Networks (TANN)cited by 18
  8. 2024Efficiently Parameterized Neural Metriplectic Systemscited by 18
  9. 2022Port-metriplectic neural networks: thermodynamics-informed machine learning of complex physical systemscited by 11
  10. 2021Physics perception in sloshing scenes with guaranteed thermodynamic consistencycited by 10
  11. 2022Thermodynamics of learning physical phenomenacited by 10
  12. 2024GFN: A graph feedforward network for resolution-invariant reduced operator learning in multifidelity applicationscited by 10
26 more
  1. 2021Interval and fuzzy physics-informed neural networks for uncertain fieldscited by 9
  2. 2022A Thermodynamics-informed Active Learning Approach to Perception and Reasoning about Fluidscited by 9
  3. 2022Evolution TANN and the identification of internal variables and evolution equations in solid mechanicscited by 9
  4. 2024A practical existence theorem for reduced order models based on convolutional autoencoderscited by 9
  5. 2021Non-intrusive Nonlinear Model Reduction via Machine Learning Approximations to Low-dimensional Operatorscited by 8
  6. 2022Approximation of nearly-periodic symplectic maps via structure-preserving neural networkscited by 6
  7. 2024A comparison of Single- and Double-generator formalisms for Thermodynamics-Informed Neural Networkscited by 4
  8. 2024PTPI-DL-ROMs: pre-trained physics-informed deep learning-based reduced order models for nonlinear parametrized PDEscited by 4
  9. 2025Deep learning-aided inverse design of porous metamaterialscited by 4
  10. 2024Thermodynamics-informed super-resolution of scarce temporal dynamics datacited by 3
  11. 2024Learning Macroscopic Dynamics from Partial Microscopic Observationscited by 3
  12. 2025A surrogate model for topology optimisation of elastic structures via parametric autoencoderscited by 3
  13. 2021Uncertainty quantification in a mechanical submodel driven by a Wasserstein-GANcited by 2
  14. 2023Uncertainty Guided Ensemble Self-Training for Semi-Supervised Global Field Reconstructioncited by 2
  15. 2024Physics-guided weak-form discovery of reduced-order models for trapped ultracold hydrodynamicscited by 2
  16. 2025Autoencoder-based non-intrusive model order reduction in continuum mechanicscited by 2
  17. 2026Surrogates for Physics-based and Data-driven Modelling of Parametric Systems: Review and New Perspectivescited by 2
  18. 2023Predicting and explaining nonlinear material response using deep Physically Guided Neural Networks with Internal Variablescited by 1
  19. 2025Variational Rank Reduction Autoencoders for Generative Thermal Designcited by 1
  20. 2026Metriplector: From Field Theory to Neural Architecturecited by 1
  21. 2026Nonlinear GENERIC-Embedded Neural Networks (N-GENNs): Learning GENERIC dynamics with non-quadratic dissipation potentialscited by 1
  22. 2025Learning thermodynamic master equations for open quantum systemscited by 0
  23. 2025Hybrid twinning using PBDW and DeepONet for the effective state estimation and prediction on partially known systemscited by 0
  24. 2025Can Transformers overcome the lack of data in the simulation of history-dependent flows?cited by 0
  25. 2026Graph-Instructed Neural Networks for parametric problems with varying boundary conditionscited by 0
  26. 2026WGFINNs: Weak formulation-based GENERIC formalism informed neural networkscited by 0