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

arXiv: https://arxiv.org/abs/2007.03758 · HTML: https://mlsanity.com/paper/2007.03758/

## Key facts

- Cited by 38 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Jul 2020.

## Built on by (most cited first, 30 of 38)

- [GFINNs: GENERIC Formalism Informed Neural Networks for Deterministic and Stochastic Dynamical Systems](https://mlsanity.com/paper/2109.00092/) (2021)
- [A graph convolutional autoencoder approach to model order reduction for parametrized PDEs](https://mlsanity.com/paper/2305.08573/) (2023)
- [Thermodynamics-informed graph neural networks](https://mlsanity.com/paper/2203.01874/) (2022)
- [The mixed deep energy method for resolving concentration features in finite strain hyperelasticity](https://mlsanity.com/paper/2104.09623/) (2021)
- [tLaSDI: Thermodynamics-informed latent space dynamics identification](https://mlsanity.com/paper/2403.05848/) (2024)
- [A deep learning energy method for hyperelasticity and viscoelasticity](https://mlsanity.com/paper/2201.08690/) (2022)
- [Efficiently Parameterized Neural Metriplectic Systems](https://mlsanity.com/paper/2405.16305/) (2024)
- [Multiscale modeling of inelastic materials with Thermodynamics-based Artificial Neural Networks (TANN)](https://mlsanity.com/paper/2108.13137/) (2021)
- [Port-metriplectic neural networks: thermodynamics-informed machine learning of complex physical systems](https://mlsanity.com/paper/2211.01873/) (2022)
- [Physics perception in sloshing scenes with guaranteed thermodynamic consistency](https://mlsanity.com/paper/2106.13301/) (2021)
- [Thermodynamics of learning physical phenomena](https://mlsanity.com/paper/2207.12749/) (2022)
- [GFN: A graph feedforward network for resolution-invariant reduced operator learning in multifidelity applications](https://mlsanity.com/paper/2406.03569/) (2024)
- [Interval and fuzzy physics-informed neural networks for uncertain fields](https://mlsanity.com/paper/2106.13727/) (2021)
- [A Thermodynamics-informed Active Learning Approach to Perception and Reasoning about Fluids](https://mlsanity.com/paper/2203.05775/) (2022)
- [Evolution TANN and the identification of internal variables and evolution equations in solid mechanics](https://mlsanity.com/paper/2209.13269/) (2022)
- [A practical existence theorem for reduced order models based on convolutional autoencoders](https://mlsanity.com/paper/2402.00435/) (2024)
- [Non-intrusive Nonlinear Model Reduction via Machine Learning Approximations to Low-dimensional Operators](https://mlsanity.com/paper/2106.09658/) (2021)
- [Approximation of nearly-periodic symplectic maps via structure-preserving neural networks](https://mlsanity.com/paper/2210.05087/) (2022)
- [A comparison of Single- and Double-generator formalisms for Thermodynamics-Informed Neural Networks](https://mlsanity.com/paper/2404.01060/) (2024)
- [PTPI-DL-ROMs: pre-trained physics-informed deep learning-based reduced order models for nonlinear parametrized PDEs](https://mlsanity.com/paper/2405.08558/) (2024)
- [Deep learning-aided inverse design of porous metamaterials](https://mlsanity.com/paper/2507.17907/) (2025)
- [Thermodynamics-informed super-resolution of scarce temporal dynamics data](https://mlsanity.com/paper/2402.17506/) (2024)
- [Learning Macroscopic Dynamics from Partial Microscopic Observations](https://mlsanity.com/paper/2410.23938/) (2024)
- [A surrogate model for topology optimisation of elastic structures via parametric autoencoders](https://mlsanity.com/paper/2507.22539/) (2025)
- [Uncertainty quantification in a mechanical submodel driven by a Wasserstein-GAN](https://mlsanity.com/paper/2110.13680/) (2021)
- [Uncertainty Guided Ensemble Self-Training for Semi-Supervised Global Field Reconstruction](https://mlsanity.com/paper/2302.11940/) (2023)
- [Physics-guided weak-form discovery of reduced-order models for trapped ultracold hydrodynamics](https://mlsanity.com/paper/2406.07519/) (2024)
- [Autoencoder-based non-intrusive model order reduction in continuum mechanics](https://mlsanity.com/paper/2509.02237/) (2025)
- [Surrogates for Physics-based and Data-driven Modelling of Parametric Systems: Review and New Perspectives](https://mlsanity.com/paper/2603.12870/) (2026)
- [Metriplector: From Field Theory to Neural Architecture](https://mlsanity.com/paper/2603.29496/) (2026)

## 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.