# Thermodynamics-informed graph neural networks for real-time simulation of digital human twins

arXiv: https://arxiv.org/abs/2412.12034 · HTML: https://mlsanity.com/paper/2412.12034/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 46 references that are in the map.
- First posted on arXiv 16 Dec 2024.

## Builds on (most cited first, 21 of 21)

- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [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)
- [A Survey of Convolutional Neural Networks: Analysis, Applications, and Prospects](https://mlsanity.com/paper/2004.02806/) (2020)
- [Structure-preserving neural networks](https://mlsanity.com/paper/2004.04653/) (2020)
- [Simulation of hyperelastic materials in real-time using Deep Learning](https://mlsanity.com/paper/1904.06197/) (2019)
- [MedShapeNet -- A Large-Scale Dataset of 3D Medical Shapes for Computer Vision](https://mlsanity.com/paper/2308.16139/) (2023)
- [MR-GNN: Multi-Resolution and Dual Graph Neural Network for Predicting Structured Entity Interactions](https://mlsanity.com/paper/1905.09558/) (2019)
- [Multiresolution Equivariant Graph Variational Autoencoder](https://mlsanity.com/paper/2106.00967/) (2021)
- [Learning Reduced-Order Models for Cardiovascular Simulations with Graph Neural Networks](https://mlsanity.com/paper/2303.07310/) (2023)
- [MGNNI: Multiscale Graph Neural Networks with Implicit Layers](https://mlsanity.com/paper/2210.08353/) (2022)
- [Digital twin, physics-based model, and machine learning applied to damage detection in structures](https://mlsanity.com/paper/2005.14360/) (2020)
- [Port-metriplectic neural networks: thermodynamics-informed machine learning of complex physical systems](https://mlsanity.com/paper/2211.01873/) (2022)
- [A Thermodynamics-informed Active Learning Approach to Perception and Reasoning about Fluids](https://mlsanity.com/paper/2203.05775/) (2022)
- [Thermodynamics-informed neural networks for physically realistic mixed reality](https://mlsanity.com/paper/2210.13414/) (2022)
- [On the feasibility of foundational models for the simulation of physical phenomena](https://mlsanity.com/paper/2410.14645/) (2024)
- [A comparison of Single- and Double-generator formalisms for Thermodynamics-Informed Neural Networks](https://mlsanity.com/paper/2404.01060/) (2024)

## Built on by (most cited first, 1 of 1)

- [Cardiovascular Digital Twins from Physics Based to Data Driven Approaches](https://mlsanity.com/paper/2608.02135/) (2026)

## Abstract (arXiv)

The growing importance of real-time simulation in the medical field has exposed the limitations and bottlenecks inherent in the digital representation of complex biological systems. This paper presents a novel methodology aimed at advancing current lines of research in soft tissue simulation. The proposed approach introduces a hybrid model that integrates the geometric bias of graph neural networks with the physical bias derived from the imposition of a metriplectic structure as soft and hard constrains in the architecture, being able to simulate hepatic tissue with dissipative properties. This approach provides an efficient solution capable of generating predictions at high feedback rate while maintaining a remarkable generalization ability for previously unseen anatomies. This makes these features particularly relevant in the context of precision medicine and haptic rendering. Based on the adopted methodologies, we propose a model that predicts human liver responses to traction and compression loads in as little as 7.3 milliseconds for optimized configurations and as fast as 1.65 milliseconds in the most efficient cases, all in the forward pass. The model achieves relative position errors below 0.15%, with stress tensor and velocity estimations maintaining relative errors under 7%. This demonstrates the robustness of the approach developed, which is capable of handling diverse load states and anatomies effectively. This work highlights the feasibility of integrating real-time simulation with patient-specific geometries through deep learning, paving the way for more robust digital human twins in medical applications.