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Generative hyperelasticity with physics-informed probabilistic diffusion fields

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Abstract

Many natural materials exhibit highly complex, nonlinear, anisotropic, and heterogeneous mechanical properties. Recently, it has been demonstrated that data-driven strain energy functions possess the flexibility to capture the behavior of these complex materials with high accuracy while satisfying physics-based constraints. However, most of these approaches disregard the uncertainty in the estimates and the spatial heterogeneity of these materials. In this work, we leverage recent advances in generative models to address these issues. We use as building block neural ordinary equations (NODE) that—by construction—create polyconvex strain energy functions, a key property of realistic hyperelastic material models. We combine this approach with probabilistic diffusion models to generate new samples of strain energy functions. This technique allows us to sample a vector of Gaussian white noise and translate it to NODE parameters thereby representing plausible strain energy functions. We extend our approach to spatially correlated diffusion resulting in heterogeneous material properties for arbitrary geometries. We extensively test our method with synthetic and experimental data on biological tissues and run finite element simulations with various degrees of spatial heterogeneity. We believe this approach is a major step forward including uncertainty in predictive, data-driven models of hyperelasticity.

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Data availability

All data, model parameters, and code associated with this study are available in a publich repository at https://github.com/tajtac/node_diffusion

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Acknowledgements

VT and IB acknowledge the support of AFOSR under the grant number FA09950-22-1-0061. FSC and MR acknowledge the support of the Open Seed Fund of the School of Engineering at Pontificia Universidad Católica de Chile. ABT acknowledges support from National Institute of Arthritis and Musculoskeletal and Skin Diseases, National Institute of Health, United States under award R01AR074525.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Purdue University, West Lafayette, IN, USA

    Vahidullah Taç, Ilias Bilionis & Adrian Buganza Tepole

  2. Department of Aerospace Engineering and Engineering Mechanics, The University of Texas at Austin, Austin, TX, USA

    Manuel K. Rausch

  3. Department of Mechanical and Metallurgical Engineering and Institute for Biological and Medical Engineering, Pontificia Universidad Catolica de Chile, Santiago, Chile

    Francisco Sahli Costabal

  4. Weldon School of Biomedical Engineering, Purdue University, West Lafayette, IN, USA

    Adrian Buganza Tepole

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  1. Vahidullah Taç
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Correspondence to Francisco Sahli Costabal or Adrian Buganza Tepole.

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Taç, V., Rausch, M.K., Bilionis, I. et al. Generative hyperelasticity with physics-informed probabilistic diffusion fields. Engineering with Computers 41, 51–69 (2025). https://doi.org/10.1007/s00366-024-01984-2

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