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GaitDynamics: a generative foundation model for analyzing human walking and running

Abstract

Understanding the dynamics of human gait, including both motions and forces, is vital to promote human mobility. While deep learning models may have advantages over costly laboratory-based experiments and physics-based simulations, existing models have been trained on small datasets with homogeneous demographics and focus on predicting a single output. We developed GaitDynamics, a generative foundation model trained on a large dataset of diverse gait patterns, which allows for flexible inputs, outputs and clinical applications. We illustrate the use of GaitDynamics for: (1) estimating ground reaction forces from kinematics with high accuracy even with missing kinematic data, (2) predicting the effects of gait modifications on knee loading without resource-intensive experiments and (3) predicting kinematic and force changes that occur with increasing running speeds. Our results demonstrate the accuracy and efficiency of GaitDynamics, showing its potential to assess and optimize gait for injury prevention, disease treatment and performance coaching. All data, code and trained models are publicly shared.

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Fig. 1: The data window and training of GaitDynamics.
Fig. 2: Force estimation using GaitDynamics with partial-body kinematics as inputs.
Fig. 3: Mean absolute errors of force estimation for the GaitDynamics model and recently published data-driven models when using full-body kinematic inputs.
Fig. 4: Mean absolute error of peak vertical force estimation when using various combinations of partial-body kinematics as inputs.
Fig. 5: Experiment-free prediction of knee adduction moment during walking with large medial–lateral trunk sway angles.
Fig. 6: Medial–lateral trunk angles and their corresponding knee adduction moments.
Fig. 7: Gait parameters across running speeds.

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Data availability

This work utilized the AddBiomechanics dataset that consists of data from 15 previous studies (https://addbiomechanics.org/download_data.html). Source data are provided with this paper.

Code availability

The trained models and source codes are available on GitHub at https://github.com/stanfordnmbl/GaitDynamics (ref. 82). We also provide a Hugging Face demo for users to upload files with full- or partial-body kinematics, predict ground reaction forces and missing kinematics using GaitDynamics, and download the results (https://huggingface.co/spaces/alanttan/GaitDynamics). Note that we used the an OpenSim Rajagopal Model without Arms (https://simtk.org/projects/full_body)68, and a different skeletal model may lead to failure due to mismatching joint names.

References

  1. Padua, D. A. & DiStefano, L. J. Sagittal plane knee biomechanics and vertical ground reaction forces are modified following ACL injury prevention programs: a systematic review. Sports Health 1, 165–173 (2009).

    Article  PubMed  PubMed Central  Google Scholar 

  2. Lieberman, D. E. et al. Foot strike patterns and collision forces in habitually barefoot versus shod runners. Nature 463, 531–535 (2010).

    Article  PubMed  CAS  Google Scholar 

  3. Sharma, S., McMorland, A. J. C. & Stinear, J. W. Stance limb ground reaction forces in high functioning stroke and healthy subjects during gait initiation. Clin. Biomech. 30, 689–695 (2015).

    Article  Google Scholar 

  4. Boehm, W. L. & Gruben, K. G. Post-stroke walking behaviors consistent with altered ground reaction force direction control advise new approaches to research and therapy. Transl. Stroke Res. 7, 3–11 (2016).

    Article  PubMed  CAS  Google Scholar 

  5. Esculier, J.-F., Bouyer, L. J. & Roy, J.-S. The effects of a multimodal rehabilitation program on symptoms and ground-reaction forces in runners with patellofemoral pain syndrome. J. Sport Rehabil. 25, 23–30 (2016).

    Article  PubMed  Google Scholar 

  6. Tan, T. et al. A scoping review of portable sensing for out-of-lab anterior cruciate ligament injury prevention and rehabilitation. npj Digit. Med. 6, 46 (2023).

    Article  PubMed  PubMed Central  Google Scholar 

  7. Andriacchi, T. P. & Mündermann, A. The role of ambulatory mechanics in the initiation and progression of knee osteoarthritis. Curr. Opin. Rheumatol. 18, 514–518 (2006).

    Article  PubMed  Google Scholar 

  8. Shull, P. B. et al. Six-week gait retraining program reduces knee adduction moment, reduces pain, and improves function for individuals with medial compartment knee osteoarthritis. J. Orthop. Res. 31, 1020–1025 (2013).

    Article  PubMed  Google Scholar 

  9. Rynne, R., Le Tong, G., Cheung, R. T. H. & Constantinou, M. Effectiveness of gait retraining interventions in individuals with hip or knee osteoarthritis: a systematic review and meta-analysis. Gait Posture 95, 164–175 (2022).

    Article  PubMed  Google Scholar 

  10. Uhlrich, S. D. et al. Six weeks of personalized gait retraining to offload the medial compartment of the knee reduces pain more than sham gait retraining. Osteoarthr. Cartil. 27, S28 (2019).

    Article  Google Scholar 

  11. Orendurff, M. S. et al. A little bit faster: lower extremity joint kinematics and kinetics as recreational runners achieve faster speeds. J. Biomech. 71, 167–175 (2018).

    Article  PubMed  Google Scholar 

  12. Haralabidis, N., Colyer, S. L., Serrancolí, G., Salo, A. I. T. & Cazzola, D. Modifications to the net knee moments lead to the greatest improvements in accelerative sprinting performance: a predictive simulation study. Sci. Rep. 12, 15908 (2022).

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  13. Piazza, S. J. Muscle-driven forward dynamic simulations for the study of normal and pathological gait. J. Neuroeng. Rehabil. 3, 5 (2006).

    Article  PubMed  PubMed Central  Google Scholar 

  14. Uhlrich, S. D., Uchida, T. K., Lee, M. R. & Delp, S. L. Ten steps to becoming a musculoskeletal simulation expert: a half-century of progress and outlook for the future. J. Biomech. 154, 111623 (2023).

    Article  PubMed  PubMed Central  Google Scholar 

  15. Dorschky, E., Nitschke, M., Seifer, A.-K., van den Bogert, A. J. & Eskofier, B. M. Estimation of gait kinematics and kinetics from inertial sensor data using optimal control of musculoskeletal models. J. Biomech. 95, 109278 (2019).

    Article  PubMed  Google Scholar 

  16. Falisse, A., Afschrift, M. & Groote, F. D. Modeling toes contributes to realistic stance knee mechanics in three-dimensional predictive simulations of walking. PLoS ONE 17, e0256311 (2022).

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  17. Ripic, Z. et al. Ground reaction force and joint moment estimation during gait using an Azure Kinect-driven musculoskeletal modeling approach. Gait Posture 95, 49–55 (2022).

    Article  PubMed  Google Scholar 

  18. Miller, R. H., Esterson, A. Y. & Shim, J. K. Joint contact forces when minimizing the external knee adduction moment by gait modification: a computer simulation study. Knee 22, 481–489 (2015).

    Article  PubMed  Google Scholar 

  19. Fregly, B. J., Reinbolt, J. A. & Chmielewski, T. L. Evaluation of a patient-specific cost function to predict the influence of foot path on the knee adduction torque during gait. Comput. Methods Biomech. Biomed. Eng. 11, 63–71 (2008).

    Article  Google Scholar 

  20. Ong, C. F., Geijtenbeek, T., Hicks, J. L. & Delp, S. L. Predicting gait adaptations due to ankle plantarflexor muscle weakness and contracture using physics-based musculoskeletal simulations. PLoS Comput. Biol. 15, e1006993 (2019).

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  21. Han, X. et al. GroundLink: a dataset unifying human body movement and ground reaction dynamics. In SIGGRAPH Asia 2023 Conference Papers 1–10 (Association for Computing Machinery, 2023).

  22. Sugai, R. et al. LSTM network-based estimation of ground reaction forces during walking in stroke patients using markerless motion capture system. IEEE Trans. Med. Robot. Bionics 5, 1016–1024 (2023).

    Article  Google Scholar 

  23. Johnson, W. R., Alderson, J., Lloyd, D. & Mian, A. Predicting athlete ground reaction forces and moments from spatio-temporal driven CNN models. IEEE Trans. Biomed. Eng. 66, 689–694 (2019).

    Article  PubMed  Google Scholar 

  24. Bergamo, G. et al. Individualized learning-based ground reaction force estimation in people post-stroke using pressure insoles. In 2023 International Conference on Rehabilitation Robotics (ICORR) 1–6 (IEEE, 2023).

  25. Donahue, S. R. & Hahn, M. E. Estimation of gait events and kinetic waveforms with wearable sensors and machine learning when running in an unconstrained environment. Sci. Rep. 13, 2339 (2023).

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  26. Bommasani, R. et al. On the opportunities and risks of foundation models. Preprint at https://doi.org/10.48550/arXiv.2108.07258 (2022).

  27. Werling, K. et al. AddBiomechanics Dataset: capturing the physics of human motion at scale. In Proc. Computer Vision – ECCV 2024 (eds Leonardis, A. et al.) 490–508 (Springer Nature, 2025).

  28. Falisse, A. et al. Rapid predictive simulations with complex musculoskeletal models suggest that diverse healthy and pathological human gaits can emerge from similar control strategies. J. R. Soc. Interface 16, 20190402 (2019).

    Article  PubMed  PubMed Central  Google Scholar 

  29. D’Hondt, L., Groote, F. D. & Afschrift, M. A dynamic foot model for predictive simulations of human gait reveals causal relations between foot structure and whole-body mechanics. PLoS Comput. Biol. 20, e1012219 (2024).

    Article  PubMed  PubMed Central  Google Scholar 

  30. Hammond, C. V. et al. The neuromusculoskeletal modeling pipeline: MATLAB-based model personalization and treatment optimization functionality for OpenSim. J. NeuroEng. Rehabil. 22, 112 (2025).

  31. Patoz, A., Lussiana, T., Breine, B., Gindre, C. & Malatesta, D. Comparison of different machine learning models to enhance sacral acceleration-based estimations of running stride temporal variables and peak vertical ground reaction force. Sports Biomech. 24, 825–841 (2025).

  32. Al-Amri, M., Al Balushi, H. & Mashabi, A. Intra-rater repeatability of gait parameters in healthy adults during self-paced treadmill-based virtual reality walking. Comput. Methods Biomech. Biomed. Eng. 20, 1669–1677 (2017).

    Article  Google Scholar 

  33. Kesar, T. M., Binder-Macleod, S. A., Hicks, G. E. & Reisman, D. S. Minimal detectable change for gait variables collected during treadmill walking in individuals post-stroke. Gait Posture 33, 314–317 (2011).

    Article  PubMed  Google Scholar 

  34. Beckerman, H. et al. Smallest real difference, a link between reproducibility and responsiveness. Qual. Life Res. 10, 571–578 (2001).

    Article  PubMed  CAS  Google Scholar 

  35. Mündermann, A., Asay, J. L., Mündermann, L. & Andriacchi, T. P. Implications of increased medio-lateral trunk sway for ambulatory mechanics. J. Biomech. 41, 165–170 (2008).

    Article  PubMed  Google Scholar 

  36. Hunt, M. A. et al. Lateral trunk lean explains variation in dynamic knee joint load in patients with medial compartment knee osteoarthritis. Osteoarthr. Cartil. 16, 591–599 (2008).

    Article  CAS  Google Scholar 

  37. Hurwitz, D. E., Ryals, A. B., Case, J. P., Block, J. A. & Andriacchi, T. P. The knee adduction moment during gait in subjects with knee osteoarthritis is more closely correlated with static alignment than radiographic disease severity, toe out angle and pain. J. Orthop. Res. 20, 101–107 (2002).

    Article  PubMed  CAS  Google Scholar 

  38. Miyazaki, T. et al. Dynamic load at baseline can predict radiographic disease progression in medial compartment knee osteoarthritis. Ann. Rheum. Dis. 61, 617–622 (2002).

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  39. Chehab, E. F., Favre, J., Erhart-Hledik, J. C. & Andriacchi, T. P. Baseline knee adduction and flexion moments during walking are both associated with 5 year cartilage changes in patients with medial knee osteoarthritis. Osteoarthr. Cartil. 22, 1833–1839 (2014).

    Article  CAS  Google Scholar 

  40. Uhlrich, S. D. et al. OpenCap: Human movement dynamics from smartphone videos. PLoS Comput. Biol. 19, e1011462 (2023).

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  41. Chung, H., Kim, J., Mccann, M. T., Klasky, M. L. & Ye, J. C. Diffusion posterior sampling for general noisy inverse problems. In The Eleventh International Conference on Learning Representations 1–30 (ICLR, 2023).

  42. Yang, L. et al. Guidance with spherical Gaussian constraint for conditional diffusion. In Proc. 41st International Conference on Machine Learning 235 56071–56095 (JMLR, 2024).

  43. Huang, W., Jiang, Y., Van Wouwe, T. & Liu, C. K. Constrained diffusion with trust sampling. Adv. Neural Inf. Process. Syst. 37, 93849–93873 (2024).

    Article  Google Scholar 

  44. Hamner, S. R. & Delp, S. L. Muscle contributions to fore-aft and vertical body mass center accelerations over a range of running speeds. J. Biomech. 46, 780–787 (2013).

    Article  PubMed  Google Scholar 

  45. Xie, Y., Jampani, V., Zhong, L., Sun, D. & Jiang, H. OmniControl: control any joint at any time for human motion generation. In The Twelfth International Conference on Learning Representations 1–19 (ICLR, 2024).

  46. Li, J. et al. DataComp-LM: in search of the next generation of training sets for language models. Adv. Neural Inf. Process. Syst. 37, 14200–14282 (2024).

    Google Scholar 

  47. Weber, M. et al. RedPajama: an open dataset for training large language models. Adv. Neural Inf. Process. Syst. 37, 116462–116492 (2024).

    Google Scholar 

  48. Tan, T., Wang, D., Shull, P. B. & Halilaj, E. IMU and smartphone camera fusion for knee adduction and knee flexion moment estimation during walking. IEEE Trans. Industr. Inform. 19, 1445–1455 (2023).

    Article  Google Scholar 

  49. Carter, J., Chen, X., Cazzola, D., Trewartha, G. & Preatoni, E. Consumer-priced wearable sensors combined with deep learning can be used to accurately predict ground reaction forces during various treadmill running conditions. PeerJ 12, e17896 (2024).

    Article  PubMed  PubMed Central  Google Scholar 

  50. Dembia, C. L., Bianco, N. A., Falisse, A., Hicks, J. L. & Delp, S. L. OpenSim Moco: musculoskeletal optimal control. PLoS Comput. Biol. 16, e1008493 (2020).

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  51. Bicer, M., Phillips, A. T. M., Melis, A., McGregor, A. H. & Modenese, L. Generative deep learning applied to biomechanics: a new augmentation technique for motion capture datasets. J. Biomech. 144, 111301 (2022).

    Article  PubMed  Google Scholar 

  52. Cotton, R. J. et al. in Predictive Intelligence in Medicine (eds Rekik, I. et al.) 277–291 (Springer Nature, 2023).

  53. Tan, T., Shull, P. B., Hicks, J. L., Uhlrich, S. D. & Chaudhari, A. S. Self-supervised learning improves accuracy and data efficiency for IMU-based ground reaction force estimation. IEEE Trans. Biomed. Eng. 71, 2095–2104 (2024).

    Article  PubMed  PubMed Central  Google Scholar 

  54. Park, J., Park, M. S., Lee, J. & Won, J. Bidirectional GaitNet: a bidirectional prediction model of human gait and anatomical conditions. In Proc. ACM SIGGRAPH 2023 Conference 1–9 (Association for Computing Machinery, 2023).

  55. Luo, S. et al. Experiment-free exoskeleton assistance via learning in simulation. Nature 630, 353–359 (2024).

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  56. Camargo, J., Ramanathan, A., Flanagan, W. & Young, A. A comprehensive, open-source dataset of lower limb biomechanics in multiple conditions of stairs, ramps, and level-ground ambulation and transitions. J. Biomech. 119, 110320 (2021).

    Article  PubMed  Google Scholar 

  57. Moore, J. K., Hnat, S. K. & van den Bogert, A. J. An elaborate data set on human gait and the effect of mechanical perturbations. PeerJ 3, e918 (2015).

    Article  PubMed  PubMed Central  Google Scholar 

  58. van der Zee, T. J., Mundinger, E. M. & Kuo, A. D. A biomechanics dataset of healthy human walking at various speeds, step lengths and step widths. Sci. Data 9, 704 (2022).

    Article  PubMed  PubMed Central  Google Scholar 

  59. Wang, H., Basu, A., Durandau, G. & Sartori, M. A wearable real-time kinetic measurement sensor setup for human locomotion. Wearable Technol. 4, e11 (2023).

    Article  PubMed  PubMed Central  Google Scholar 

  60. Carter, J., Chen, X., Cazzola, D., Trewartha, G. & Preatoni, E. Full Body Kinematics and Ground Reaction Forces of Fifty Heterogeneous Runners Completing Treadmill Running at Various Speeds and Gradients (Univ. Bath, 2024).

  61. Tan, T., Strout, Z. A., Cheung, R. T. H. & Shull, P. B. Strike index estimation using a convolutional neural network with a single, shoe-mounted inertial sensor. J. Biomech. 139, 111145 (2022).

    Article  PubMed  Google Scholar 

  62. Falisse, A., Van Rossom, S., Jonkers, I. & De Groote, F. EMG-driven optimal estimation of subject-specific Hill Model muscle–tendon parameters of the knee joint actuators. IEEE Trans. Biomed. Eng. 64, 2253–2262 (2017).

    Article  PubMed  Google Scholar 

  63. Lencioni, T., Carpinella, I., Rabuffetti, M., Marzegan, A. & Ferrarin, M. Human kinematic, kinetic and EMG data during different walking and stair ascending and descending tasks. Sci. Data 6, 309 (2019).

    Article  PubMed  PubMed Central  Google Scholar 

  64. Fregly, B. J. et al. Grand challenge competition to predict in vivo knee loads. J. Orthop. Res. 30, 503–513 (2012).

    Article  PubMed  Google Scholar 

  65. Li, G., Shourijeh, M. S., Ao, D., Patten, C. & Fregly, B. J. How well do commonly used co-contraction indices approximate lower limb joint stiffness trends during gait for individuals post-stroke? Front. Bioeng. Biotechnol. 8, 588908 (2021).

    Article  PubMed  PubMed Central  Google Scholar 

  66. dos Santos, D. A., Fukuchi, C. A., Fukuchi, R. K. & Duarte, M. A data set with kinematic and ground reaction forces of human balance. PeerJ 5, e3626 (2017).

    Article  PubMed  PubMed Central  Google Scholar 

  67. Werling, K. et al. AddBiomechanics: automating model scaling, inverse kinematics, and inverse dynamics from human motion data through sequential optimization. PLoS ONE 18, e0295152 (2023).

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  68. Rajagopal, A. et al. Full-body musculoskeletal model for muscle-driven simulation of human gait. IEEE Trans. Biomed. Eng. 63, 2068–2079 (2016).

    Article  PubMed  PubMed Central  Google Scholar 

  69. Seth, A. et al. OpenSim: simulating musculoskeletal dynamics and neuromuscular control to study human and animal movement. PLoS Comput. Biol. 14, e1006223 (2018).

    Article  PubMed  PubMed Central  Google Scholar 

  70. de Boor, C. On calculating with B-splines. J. Approx. Theory 6, 50–62 (1972).

    Article  Google Scholar 

  71. Jazar, R. N. in Theory of Applied Robotics: Kinematics, Dynamics, and Control (ed. Jazar, R. N.) 361–413 (Springer, 2022).

  72. Zhou, Y., Barnes, C., Lu, J., Yang, J. & Li, H. On the continuity of rotation representations in neural networks. In 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) 5738–5746 (IEEE, 2019).

  73. Leskinen, A., Häkkinen, K., Virmavirta, M., Isolehto, J. & Kyröläinen, H. Comparison of running kinematics between elite and national-standard 1500-m runners. Sports Biomech. 8, 1–9 (2009).

    Article  PubMed  Google Scholar 

  74. Van Wouwe, T., Lee, S., Falisse, A., Delp, S. & Liu, C. K. DiffusionPoser: real-time human motion reconstruction from arbitrary sparse sensors using autoregressive diffusion. In 2024 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) 2513–2523 (IEEE, 2024).

  75. Tseng, J., Castellon, R. & Liu, C. K. EDGE: editable dance generation from music. In 2023 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) 448–458 (IEEE, 2023).

  76. Ho, J., Jain, A. & Abbeel, P. Denoising diffusion probabilistic models. In Proc. 34th International Conference on Neural Information Processing Systems 6840–6851 (Curran Associates, 2020).

  77. Su, J. et al. RoFormer: enhanced transformer with rotary position embedding. Neurocomputing 568, 127063 (2024).

    Article  Google Scholar 

  78. Xie, X., Zhou, P., Li, H., Lin, Z. & Yan, S. Adan: adaptive Nesterov momentum algorithm for faster optimizing deep models. IEEE Trans. Pattern Anal. Mach. Intell. 46, 9508–9520 (2024).

    Article  PubMed  Google Scholar 

  79. Song, J., Meng, C. & Ermon, S. Denoising diffusion implicit models. In International Conference on Learning Representations Poster (ICLR, 2021).

  80. Lugmayr, A. et al. RePaint: inpainting using denoising diffusion probabilistic models. In 2022 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) 11461–11471 (IEEE, 2022).

  81. Rutherford, D. J. & Baker, M. Knee moment outcomes using inverse dynamics and the cross product function in moderate knee osteoarthritis gait: a comparison study. J. Biomech. 78, 150–154 (2018).

    Article  PubMed  Google Scholar 

  82. Tan, T. GaitDynamics. GitHub https://github.com/stanfordnmbl/GaitDynamics (2025).

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Acknowledgements

This work was supported by the Joe and Clara Tsai Foundation through the Wu Tsai Human Performance Alliance, and by the US National Institutes of Health (NIH) under Grants P50 HD118632, P41 EB027060, P2C HD101913, R01 AR077604, R01 EB002524 and R01 AR079431.

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All authors contributed to the conception of the work. T.T., T.V.W. and K.F.W. worked on data analysis. T.T. drafted the manuscript. All authors critically revised the manuscript and approved the final version.

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Correspondence to Tian Tan.

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Tan, T., Van Wouwe, T., Werling, K.F. et al. GaitDynamics: a generative foundation model for analyzing human walking and running. Nat. Biomed. Eng (2026). https://doi.org/10.1038/s41551-025-01565-8

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