mlsanityData to 7 Oct 2026

Simulation of hyperelastic materials in real-time using Deep Learning

arXiv 1904.06197 ↗First posted 10 Apr 2019cs.CE cs.LG physics.comp-phcited by 35

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Abstract (arXiv)

The finite element method (FEM) is among the most commonly used numerical methods for solving engineering problems. Due to its computational cost, various ideas have been introduced to reduce computation times, such as domain decomposition, parallel computing, adaptive meshing, and model order reduction. In this paper we present U-Mesh: a data-driven method based on a U-Net architecture that approximates the non-linear relation between a contact force and the displacement field computed by a FEM algorithm. We show that deep learning, one of the latest machine learning methods based on artificial neural networks, can enhance computational mechanics through its ability to encode highly non-linear models in a compact form. Our method is applied to two benchmark examples: a cantilever beam and an L-shape subject to moving punctual loads. A comparison between our method and proper orthogonal decomposition (POD) is done through the paper. The results show that U-Mesh can perform very fast simulations on various geometries, mesh resolutions and number of input forces with very small errors.

Key facts. Cited by 35 papers in the map (data through 7 Oct 2026). First posted on arXiv 10 Apr 2019.

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Citing papers per year: 2021: 5; 2022: 10; 2023: 5; 2024: 4; 2025: 4; 2026: 7.

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  2. 2021A Comprehensive Review of Computer-aided Whole-slide Image Analysis: from Datasets to Feature Extraction, Segmentation, Classification, and Detection Approachescited by 44
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  4. 2022MAgNET: A Graph U-Net Architecture for Mesh-Based Simulationscited by 26
  5. 2022Physics-Guided, Physics-Informed, and Physics-Encoded Neural Networks in Scientific Computingcited by 24
  6. 2022Label fusion and training methods for reliable representation of inter-rater uncertaintycited by 13
  7. 2021Probabilistic Deep Learning for Real-Time Large Deformation Simulationscited by 11
  8. 2021Predicting Mechanically Driven Full-Field Quantities of Interest with Deep Learning-Based Metamodelscited by 10
  9. 2022AWSnet: An Auto-weighted Supervision Attention Network for Myocardial Scar and Edema Segmentation in Multi-sequence Cardiac Magnetic Resonance Imagescited by 10
  10. 2021DeepPhysics: a physics aware deep learning framework for real-time simulationcited by 6
  11. 2023Real-time simulation of viscoelastic tissue behavior with physics-guided deep learningcited by 6
  12. 2022Convolution, aggregation and attention based deep neural networks for accelerating simulations in mechanicscited by 5
23 more
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  2. 2025A Physics-Informed Meta-Learning Framework for the Continuous Solution of Parametric PDEs on Arbitrary Geometriescited by 5
  3. 2026Artificial Intelligence in Materials Science and Engineering: Current Landscape, Key Challenges, and Future Trajectoriecited by 5
  4. 2021Automated liver tissues delineation techniques: A systematic survey on machine learning current trends and future orientationscited by 3
  5. 2022Analytically Integratable Zero-restlength Springs for Capturing Dynamic Modes unrepresented by Quasistatic Neural Networkscited by 2
  6. 2022Stochastic Modeling of Inhomogeneities in the Aortic Wall and Uncertainty Quantification using a Bayesian Encoder-Decoder Surrogatecited by 2
  7. 2024Thermodynamics-informed graph neural networks for real-time simulation of digital human twinscited by 1
  8. 2025Neural-Augmented Kelvinlet for Real-Time Soft Tissue Deformation Modelingcited by 1
  9. 2025MTCNet: Motion and Topology Consistency Guided Learning for Mitral Valve Segmentationin 4D Ultrasoundcited by 1
  10. 2025Conditional Graph Neural Network for Predicting Soft Tissue Deformation and Forcescited by 1
  11. 2026A Hybrid Conditional Diffusion-DeepONet Framework for High-Fidelity Stress Prediction in Hyperelastic Materialscited by 1
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  13. 2023Cross-head mutual Mean-Teaching for semi-supervised medical image segmentationcited by 0
  14. 2023Diagonal Hierarchical Consistency Learning for Semi-supervised Medical Image Segmentationcited by 0
  15. 2023PerSival: Neural-network-based visualisation for pervasive continuum-mechanical simulations in musculoskeletal biomechanicscited by 0
  16. 2024STMPL: Human Soft-Tissue Simulationcited by 0
  17. 2024Automatic diagnosis of cardiac magnetic resonance images based on semi-supervised learningcited by 0
  18. 2024Dual-Teacher Ensemble Models with Double-Copy-Paste for 3D Semi-Supervised Medical Image Segmentationcited by 0
  19. 2026Autoregressive deep learning for real-time simulation of soft tissue dynamics during virtual neurosurgerycited by 0
  20. 2026Data-driven registration and modeling of brain deformation for image-guided neurosurgerycited by 0
  21. 2026HyperShape: Hyperelasticity Across Diverse Shapescited by 0
  22. 2026Generalizing Soft Tissue Deformation and Force Prediction Across Material Stiffness and Geometrycited by 0
  23. 2026DeepFEAv2: Deep Learning for Transient Finite Element Analysis Beyond Structured Meshescited by 0