Automated model discovery for human brain using Constitutive Artificial Neural Networks

Linka, Kevin; Pierre, Sarah R. St.; Kuhl, Ellen

doi:10.1016/j.actbio.2023.01.055

Cited by 36 publications

(54 citation statements)

References 58 publications

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“…When using biaxial extension experiments, the first and second invariant are no longer identical and the model consistently favors the second invariant over the first. Taken together, in agreement with previous observations [43, 56], we find that the second invariant is better suited to capture the isotropic response of biological tissues [34] and describes the experimental data more accurately than the first.…”

Section: Discussionsupporting

confidence: 92%

“…By constraining the majority of weights to zero and only training for a selective subset of weights [43], we can utilize our neural network to identify the parameters of popular classical constitutive models. As a matter of fact, our neural network in Figure 1 is a generalization of previous invariant-based neural networks for isotropic materials [43] and for transversely isotropic materials [44] and naturally captures all their features as special cases. As such, we can reduce it to represent popular isotropic models including the neo Hooke [68], Blatz Ko [8], Mooney Rivlin [49, 58], or Demiray [12] models, as well as transversely isotropic models including the Lanir [39], Weiss [71], Groves [25], or Holzapfel [31] models.…”

Section: Discussionmentioning

confidence: 99%

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Automated model discovery for human cardiac tissue: Discovering the best model and parameters

Martonová,

Peirlinck,

Linka

et al. 2024

Preprint

Self Cite

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For more than half a century, scientists have developed mathematical models to understand the behavior of the human heart. Today, we have dozens of heart tissue models to choose from, but selecting the best model is limited to expert professionals, prone to user bias, and vulnerable to human error. Here we take the human out of the loop and automate the process of model discovery. Towards this goal, we establish a novel incompressible orthotropic constitutive neural network to simultaneously discover both, model and parameters, that best explain human cardiac tissue. Notably, our network features 32 individual terms, 8 isotropic and 24 anisotropic, and fully autonomously selects the best model, out of more than 4 billion possible combinations of terms. We demonstrate that we can successfully train the network with triaxial shear and biaxial extension tests and systematically sparsify the parameter vector withL1-regularization. Strikingly, we robustly discover a four-term model that features a quadratic term in the second invariantI2, and exponential quadratic terms in the fourth and eighth invariantsI4f,I4n, andI8fs. Importantly, our discovered model is interpretable by design and has parameters with well-defined physical units. We show that it outperforms popular existing myocardium models and generalizes well, from homogeneous laboratory tests to heterogeneous whole heart simulations. This is made possible by a new universal material subroutine that directly takes the discovered network weights as input. Automating the process of model discovery has the potential to democratize cardiac modeling, broaden participation in scientific discovery, and accelerate the development of innovative treatments for cardiovascular disease.Our source code, data, and examples are available athttps://github.com/LivingMatterLab/CANN.

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Section: Discussionsupporting

confidence: 92%

Section: Discussionmentioning

confidence: 99%

Automated model discovery for human cardiac tissue: Discovering the best model and parameters

Martonová,

Peirlinck,

Linka

et al. 2024

Preprint

Self Cite

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“…Constitutive neural networks. Motivated by these kinematic and constitutive considerations, we reverse-engineer our own constitutive neural network that satisfies the conditions of thermodynamic consistency, material objectivity, material symmetry, incompressibility, constitutive restrictions, and polyconvexity by design [28,39]. Yet, instead of building these constraints into the loss function, we hardwire them directly into our network input, output, architecture, and activation functions [40,41] to satisfy the fundamental laws of physics.…”

Section: Methodsmentioning

confidence: 99%

“…Yet, instead of building these constraints into the loss function, we hardwire them directly into our network input, output, architecture, and activation functions [40, 41] to satisfy the fundamental laws of physics. Special members of this family represent well-known constitutive models, including the neo Hooke [31], Blatz Ko [29], Mooney Rivlin [32, 33], and Demiray [30] models, for which the network weights gain a clear physical interpretation [39, 42]. Specifically, our constitutive neural network learns a free energy function that is parameterized in terms of the first and second invariants.…”

Section: Methodsmentioning

confidence: 99%

Got meat? The mechanical signature of plant-based and animal meat

St. Pierre,

Darwin,

Adil

et al. 2024

Preprint

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Eating less meat is associated with a healthier body and planet. Yet, we remain reluctant to switch to a plant-based diet, largely due to the sensory experience of plant-based meat. The gold standard test to analyze the texture of food is the double mechanical compression test, but it only characterizes one-dimensional behavior. Here we use tension, compression, and shear tests along with a constitutive neural network to automatically characterize the mechanics of eight plant- and animal-based meats across the entire three-dimensional spectrum. We discover that plant-based sausage and hotdog, with stiffnesses from 35.3kPa to 106.3kPa, successfully mimic the behavior of their animal counterparts, with stiffnesses from 26.8kPa to 115.5kPa, while tofurky with 167.9kPa to 224.5kPa is twice as stiff, and tofu with 22.3kPa to 34.0kPa is twice as soft. Strikingly, the more processed the product--with more additives and ingredients--the more complex the mechanics: The best model for the softest, simplest, and oldest product, plain tofu, is the simplest, the classical neo Hooke model; the best model for the stiffest products, tofurky and plant sausage, is the popular Mooney Rivlin model; the best models for all highly processed real meat products are more complex with quadratic and exponential terms. Interestingly, all animal products are stiffer in tension than in compression, while all plant-based products, except for extra firm tofu, are stiffer in compression. Our results suggest that probing the fully three-dimensional mechanics of plant- and animal-based meats is critical to understand subtle differences in texture that may result in a different perception of taste. We anticipate our models to be a first step towards using generative artificial intelligence to scientifically reverse-engineer formulas for plant-based meat products with customer-friendly tunable properties.

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“…Such models are precious in fields where highly flexible yet physically sensible models are required, such as the simulation of microstructured materials (Gärtner et al, 2021; Kumar and Kochmann, 2022; Kalina et al, 2023). Furthermore, including mechanical conditions improves the model generalization (Klein et al, 2022b), allowing for model calibrations with sparse data usually available from real-world experiments (Linka et al, 2023). For the construction of polyconvex potentials, several approaches exist (Chen and Guilleminot, 2022; Klein et al, 2022a; Tac et al, 2022), where the most noteworthy approaches are based on input-convex neural networks (ICNNs).…”

Section: Introductionmentioning

confidence: 99%

Parametrized polyconvex hyperelasticity with physics-augmented neural networks

Klein,

Roth,

Valizadeh

et al. 2023

DCE

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In the present work, neural networks are applied to formulate parametrized hyperelastic constitutive models. The models fulfill all common mechanical conditions of hyperelasticity by construction. In particular, partially input convex neural network (pICNN) architectures are applied based on feed-forward neural networks. Receiving two different sets of input arguments, pICNNs are convex in one of them, while for the other, they represent arbitrary relationships which are not necessarily convex. In this way, the model can fulfill convexity conditions stemming from mechanical considerations without being too restrictive on the functional relationship in additional parameters, which may not necessarily be convex. Two different models are introduced, where one can represent arbitrary functional relationships in the additional parameters, while the other is monotonic in the additional parameters. As a first proof of concept, the model is calibrated to data generated with two differently parametrized analytical potentials, whereby three different pICNN architectures are investigated. In all cases, the proposed model shows excellent performance.

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Automated model discovery for human brain using Constitutive Artificial Neural Networks

Cited by 36 publications

References 58 publications

Automated model discovery for human cardiac tissue: Discovering the best model and parameters

Automated model discovery for human cardiac tissue: Discovering the best model and parameters

Got meat? The mechanical signature of plant-based and animal meat

Parametrized polyconvex hyperelasticity with physics-augmented neural networks

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