Physics-informed graph neural network emulation of soft-tissue mechanics

Dalton, David; Husmeier, Dirk; Gao, Hao

doi:10.1016/j.cma.2023.116351

Cited by 12 publications

(4 citation statements)

References 48 publications

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“…Self-supervised methods: In another line of research, [20][21][22][23] graph neural networks have demonstrated significant potential for modeling dynamic physical systems, emerging as a primary model consideration in constructing self-supervised training frameworks in recent years. The most relevant work to ours is Reference 22, which introduces repeated message passing blocks, MeshGraphNets (MGN), to learn the propagation of dynamic information in physical systems, such as fluids, cloth, soft bodies and so forth.…”

Section: Learning-based Methodsmentioning

confidence: 99%

“…MGN module has been proven to have powerful modeling capabilities for various dynamic physical systems, including cloth, 21 fluid, 26 biological soft tissue 20 and so forth. However, to our knowledge, we are the first to employ MGN blocks in constructing an self-supervised neural network framework within the domain of 3D character secondary motion.…”

Section: Learning-based Methodsmentioning

confidence: 99%

“…The neo‐Hookean model was found to be more effective than the commonly used St. Venant‐Kirchhoff (StVK) model in our experiments, marking the first introduction of the neo‐Hookean model into neural secondary motion as a supervisory method. According to Reference 20, the strain potential energy due to deformation is expressed as:

\begin{array}{ll}\hfill {\mathcal{L}}_{\mathrm{strain}}& =\sum \limits_{el=1}^n\Psi \left({F}^{el}\right){V}^{el},\\ {}\hfill \Psi & =\frac{1}{2}\lambda {\left(\log |\det \left(\boldsymbol{F}\right)|\right)}^2-\\ {}\hfill & \kern1em \mu \log \mid \det \left(\boldsymbol{F}\right)\mid +\frac{1}{2}\mu \left(\mathrm{tr}\left({\boldsymbol{F}}^{\mathrm{T}}\boldsymbol{F}\right)-3\right),\end{array}

with

\lambda

and

\mu

as the material's Lamé constants,

{F}^{el}

represents the deformation gradient matrix for the element,

\Psi \left({F}^{el}\right)

is the strain energy density of the element, and

V^{e l}

…”

Section: Methodsmentioning

confidence: 99%

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Multi‐scale edge aggregation mesh‐graph‐network for character secondary motion

Wang,

Liu

2024

Computer Animation & Virtual

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As an enhancement to skinning‐based animations, light‐weight secondary motion method for 3D characters are widely demanded in many application scenarios. To address the dependence of data‐driven methods on ground truth data, we propose a self‐supervised training strategy that is free of ground truth data for the first time in this domain. Specifically, we construct a self‐supervised training framework by modeling the implicit integration problem with steps as an optimization problem based on physical energy terms. Furthermore, we introduce a multi‐scale edge aggregation mesh‐graph block (MSEA‐MG Block), which significantly enhances the network performance. This enables our model to make vivid predictions of secondary motion for 3D characters with arbitrary structures. Empirical experiments indicate that our method, without requiring ground truth data for model training, achieves comparable or even superior performance quantitatively and qualitatively compared to state‐of‐the‐art data‐driven approaches in the field.

show abstract

Section: Learning-based Methodsmentioning

confidence: 99%

Section: Learning-based Methodsmentioning

confidence: 99%

\begin{array}{ll}\hfill {\mathcal{L}}_{\mathrm{strain}}& =\sum \limits_{el=1}^n\Psi \left({F}^{el}\right){V}^{el},\\ {}\hfill \Psi & =\frac{1}{2}\lambda {\left(\log |\det \left(\boldsymbol{F}\right)|\right)}^2-\\ {}\hfill & \kern1em \mu \log \mid \det \left(\boldsymbol{F}\right)\mid +\frac{1}{2}\mu \left(\mathrm{tr}\left({\boldsymbol{F}}^{\mathrm{T}}\boldsymbol{F}\right)-3\right),\end{array}

with

\lambda

and

\mu

as the material's Lamé constants,

{F}^{el}

represents the deformation gradient matrix for the element,

\Psi \left({F}^{el}\right)

is the strain energy density of the element, and

V^{e l}

…”

Section: Methodsmentioning

confidence: 99%

See 1 more Smart Citation

Multi‐scale edge aggregation mesh‐graph‐network for character secondary motion

Wang,

Liu

2024

Computer Animation & Virtual

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show abstract

“…By representing the meshes as graphs where graph vertices and edges represent mesh nodes and edges, previous works have shown the capability of GNNs in learning to simulate soft tissue mechanics while generalizing to new geometries (DALTON; HUSMEIER; GAO, 2023;HUSMEIER, 2022). Other successful cases are using these models to solve PDE-governed forward and inverse problems (GAO; ZAHR; WANG, 2022) and predicting dynamic responses of continuous deformable bodies (CHEN et al, 2024).…”

Section: List Of Abreviations Introductionmentioning

confidence: 99%