# Real-time simulation of viscoelastic tissue behavior with physics-guided deep learning

arXiv: https://arxiv.org/abs/2301.04614 · HTML: https://mlsanity.com/paper/2301.04614/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 35 references that are in the map.
- First posted on arXiv 11 Jan 2023.

## Builds on (most cited first, 5 of 5)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Theory-guided Data Science: A New Paradigm for Scientific Discovery from Data](https://mlsanity.com/paper/1612.08544/) (2016)
- [Physics-Guided Machine Learning for Scientific Discovery: An Application in Simulating Lake Temperature Profiles](https://mlsanity.com/paper/2001.11086/) (2020)
- [Simulation of hyperelastic materials in real-time using Deep Learning](https://mlsanity.com/paper/1904.06197/) (2019)
- [Learning Soft Tissue Behavior of Organs for Surgical Navigation with Convolutional Neural Networks](https://mlsanity.com/paper/1904.00722/) (2019)

## Built on by (most cited first, 6 of 6)

- [A Review on Organ Deformation Modeling Approaches for Reliable Surgical Navigation using Augmented Reality](https://mlsanity.com/paper/2408.02713/) (2024)
- [ShuttleSHAP: A Turn-Based Feature Attribution Approach for Analyzing Forecasting Models in Badminton](https://mlsanity.com/paper/2312.10942/) (2023)
- [STMPL: Human Soft-Tissue Simulation](https://mlsanity.com/paper/2403.08344/) (2024)
- [PhysSFI-Net: Physics-informed Geometric Learning of Skeletal and Facial Interactions for Orthognathic Surgical Outcome Prediction](https://mlsanity.com/paper/2601.02088/) (2026)
- [Autoregressive deep learning for real-time simulation of soft tissue dynamics during virtual neurosurgery](https://mlsanity.com/paper/2601.13676/) (2026)
- [Deep learning-based prediction of time-resolved adhesive forces in viscoelastic Hertzian contacts](https://mlsanity.com/paper/2607.19060/) (2026)

## Abstract (arXiv)

Finite element methods (FEM) are popular approaches for simulation of soft tissues with elastic or viscoelastic behavior. However, their usage in real-time applications, such as in virtual reality surgical training, is limited by computational cost. In this application scenario, which typically involves transportable simulators, the computing hardware severely constrains the size or the level of details of the simulated scene. To address this limitation, data-driven approaches have been suggested to simulate mechanical deformations by learning the mapping rules from FEM generated datasets. Herein, we propose a deep learning method for predicting displacement fields of soft tissues with viscoelastic properties. The main contribution of this work is the use of a physics-guided loss function for the optimization of the deep learning model parameters. The proposed deep learning model is based on convolutional (CNN) and recurrent layers (LSTM) to predict spatiotemporal variations. It is augmented with a mass conservation law in the lost function to prevent the generation of physically inconsistent results. The deep learning model is trained on a set of FEM datasets that are generated from a commercially available state-of-the-art numerical neurosurgery simulator. The use of the physics-guided loss function in a deep learning model has led to a better generalization in the prediction of deformations in unseen simulation cases. Moreover, the proposed method achieves a better accuracy over the conventional CNN models, where improvements were observed in unseen tissue from 8% to 30% depending on the magnitude of external forces. It is hoped that the present investigation will help in filling the gap in applying deep learning in virtual reality simulators, hence improving their computational performance (compared to FEM simulations) and ultimately their usefulness.