# A comparison of Single- and Double-generator formalisms for Thermodynamics-Informed Neural Networks

arXiv: https://arxiv.org/abs/2404.01060 · HTML: https://mlsanity.com/paper/2404.01060/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 39 references that are in the map.
- First posted on arXiv 1 Apr 2024.

## Builds on (most cited first, 17 of 17)

- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next](https://mlsanity.com/paper/2201.05624/) (2022)
- [Physics-informed neural networks (PINNs) for fluid mechanics: A review](https://mlsanity.com/paper/2105.09506/) (2021)
- [Lagrangian Neural Networks](https://mlsanity.com/paper/2003.04630/) (2020)
- [Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1711.10561/) (2017)
- [Structure-preserving neural networks](https://mlsanity.com/paper/2004.04653/) (2020)
- [Dissipative Hamiltonian Neural Networks: Learning Dissipative and Conservative Dynamics Separately](https://mlsanity.com/paper/2201.10085/) (2022)
- [A graph convolutional autoencoder approach to model order reduction for parametrized PDEs](https://mlsanity.com/paper/2305.08573/) (2023)
- [Deep learning of thermodynamics-aware reduced-order models from data](https://mlsanity.com/paper/2007.03758/) (2020)
- [OnsagerNet: Learning Stable and Interpretable Dynamics using a Generalized Onsager Principle](https://mlsanity.com/paper/2009.02327/) (2020)
- [Hamiltonian neural networks for solving equations of motion](https://mlsanity.com/paper/2001.11107/) (2020)
- [Thermodynamics-informed graph neural networks](https://mlsanity.com/paper/2203.01874/) (2022)
- [Self-Supervised Learning with Lie Symmetries for Partial Differential Equations](https://mlsanity.com/paper/2307.05432/) (2023)
- [Reversible and irreversible bracket-based dynamics for deep graph neural networks](https://mlsanity.com/paper/2305.15616/) (2023)
- [Model Reduction with Memory and the Machine Learning of Dynamical Systems](https://mlsanity.com/paper/1808.04258/) (2018)
- [Thermodynamics of learning physical phenomena](https://mlsanity.com/paper/2207.12749/) (2022)

## Built on by (most cited first, 4 of 4)

- [Thermodynamics-informed graph neural networks for real-time simulation of digital human twins](https://mlsanity.com/paper/2412.12034/) (2024)
- [Application of Reduced-Order Models for Temporal Multiscale Representations in the Prediction of Dynamical Systems](https://mlsanity.com/paper/2510.18925/) (2025)
- [Nonlinear GENERIC-Embedded Neural Networks (N-GENNs): Learning GENERIC dynamics with non-quadratic dissipation potentials](https://mlsanity.com/paper/2605.09058/) (2026)
- [Can Transformers overcome the lack of data in the simulation of history-dependent flows?](https://mlsanity.com/paper/2512.16305/) (2025)

## Abstract (arXiv)

The development of inductive biases has been shown to be a very effective way to increase the accuracy and robustness of neural networks, particularly when they are used to predict physical phenomena. These biases significantly increase the certainty of predictions, decrease the error made and allow considerably smaller datasets to be used. There are a multitude of methods in the literature to develop these biases. One of the most effective ways, when dealing with physical phenomena, is to introduce physical principles of recognised validity into the network architecture. The problem becomes more complex without knowledge of the physical principles governing the phenomena under study. A very interesting possibility then is to turn to the principles of thermodynamics, which are universally valid, regardless of the level of abstraction of the description sought for the phenomenon under study. To ensure compliance with the principles of thermodynamics, there are formulations that have a long tradition in many branches of science. In the field of rheology, for example, two main types of formalisms are used to ensure compliance with these principles: one-generator and two-generator formalisms. In this paper we study the advantages and disadvantages of each, using classical problems with known solutions and synthetic data.