PhysGNN: A Physics-Driven Graph Neural Network Based Model for Predicting Soft Tissue Deformation in Image-Guided Neurosurgery

Salehi, Yasmin; Giannacopoulos, Dennis D.

doi:10.48550/arxiv.2109.04352

Cited by 2 publications

(2 citation statements)

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“…Such approaches are particularly common in virtual surgery applications, e.g. [De et al 2011;Liu et al 2020;Pfeiffer et al 2019;Roewer-Despres et al 2018;Salehi and Giannacopoulos 2021]. [Jin et al 2020] trains a CNN to infer a displacement map which adds wrinkles to skinned cloth, and [Wu et al 2020] improves the accuracy of this approach by embedding the cloth into a volumetric tetrahedral mesh.…”

Section: Related Workmentioning

confidence: 99%

Analytically Integratable Zero-restlength Springs for Capturing Dynamic Modes unrepresented by Quasistatic Neural Networks

Jin¹,

Han²,

Geng³

et al. 2022

Preprint

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Section: Related Workmentioning

confidence: 99%

Analytically Integratable Zero-restlength Springs for Capturing Dynamic Modes unrepresented by Quasistatic Neural Networks

Jin¹,

Han²,

Geng³

et al. 2022

Preprint

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“…These weaker physics constraints are either implemented by means of convolution-like operators representing derivatives up to a particular degree, for example, PDE-Net (Long et al, 2018), PhyDNet (consisting of a data-driven ConvLSTM and a physics-constrained path) proposed by Guen and Thome (2020), or SIREN (Sitzmann et al, 2020); or by directly learning the transition function 𝐴𝐴 𝐴𝐴 ∶ ℝ 𝑑𝑑 ↦ℝ 𝑑𝑑 (e.g., in form of a vector field) that maps the d-dimensional observation in frame t to the succeeding frame t + 1 (De Bézenac et al, 2019;Tran & Ward, 2017). More recently, graph-based approaches are formulated by Seo et al (2019) and Salehi and Giannacopoulos (2021) to explicitly consider differences between neighboring control volumes on spatially irregularly distributed data.…”

mentioning

confidence: 99%

Learning Groundwater Contaminant Diffusion‐Sorption Processes With a Finite Volume Neural Network

Praditia

Karlbauer

Otte

et al. 2022

Water Resources Research

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Improved understanding of complex hydrosystem processes is key to advance water resources research. Nevertheless, the conventional way of modeling these processes suffers from a high conceptual uncertainty, due to almost ubiquitous simplifying assumptions used in model parameterizations/closures. Machine learning (ML) models are considered as a potential alternative, but their generalization abilities remain limited. For example, they normally fail to predict accurately across different boundary conditions. Moreover, as a black box, they do not add to our process understanding or to discover improved parameterizations/closures. To tackle this issue, we propose the hybrid modeling framework FINN (finite volume neural network). It merges existing numerical methods for partial differential equations (PDEs) with the learning abilities of artificial neural networks (ANNs). FINN is applied on discrete control volumes and learns components of the investigated system equations, such as numerical stencils, model parameters, and arbitrary closure/constitutive relations. Consequently, FINN yields highly interpretable results. We demonstrate FINN's potential on a diffusion‐sorption problem in clay. Results on numerically generated data show that FINN outperforms other ML models when tested under modified boundary conditions, and that it can successfully differentiate between the usual, known sorption isotherms. Moreover, we also equip FINN with uncertainty quantification methods to lay open the total uncertainty of scientific learning, and then apply it to a laboratory experiment. The results show that FINN performs better than calibrated PDE‐based models as it is able to flexibly learn and model sorption isotherms without being restricted to choose among available parametric models.

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PhysGNN: A Physics-Driven Graph Neural Network Based Model for Predicting Soft Tissue Deformation in Image-Guided Neurosurgery

Cited by 2 publications

References 0 publications

Analytically Integratable Zero-restlength Springs for Capturing Dynamic Modes unrepresented by Quasistatic Neural Networks

Analytically Integratable Zero-restlength Springs for Capturing Dynamic Modes unrepresented by Quasistatic Neural Networks

Learning Groundwater Contaminant Diffusion‐Sorption Processes With a Finite Volume Neural Network

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