Machine learning-assisted parameter identification for constitutive models based on concatenated loading path sequences

Schulte, Robin; Karca, Cavid; Ostwald, Richard; Menzel, Andreas

doi:10.1016/j.euromechsol.2022.104854

Cited by 24 publications

(9 citation statements)

References 35 publications

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“…Here, instead of approximating the tensor-valued tensor function P ( F ) directly through a classical neural network [14, 36, 47], our objective is to design a Constitutive Artificial Neural Network that limits the space of admissible functions by a priori guaranteeing common thermodynamic and physical constraints:…”

Section: Constitutive Modelingmentioning

confidence: 99%

Automated model discovery for skin: Discovering the best model, data, and experiment

Linka

Tepole

Holzapfel

et al. 2022

Preprint

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Choosing the best constitutive model and the right set of model parameters is at the heart of continuum mechanics. For decades, the gold standard in constitutive modeling has been to first select a model and then fit its parameters to data. However, the success of this approach is highly dependent on user experience and personal preference. Here we propose a new method that simultaneously and fully autonomously discovers the best model and parameters to explain experimental data. Mathematically, the model finding is translated into a complex non-convex optimization problem. We solve this problem by formulating it as a neural network, and leveraging the success, robustness, and stability of the optimization tools developed in classical neural network modeling. Instead of using a classical off-the-shelf neural network, we design a new family of Constitutive Artificial Neural Networks with activation functions that feature popular constitutive models and parameters that have a clear physical interpretation. Our new network inherently satisfies general kinematic, thermodynamic, and physical constraints and trains robustly, even with sparse data. We illustrate its potential for biaxial extension experiments on skin and demonstrate that the majority of network weights train to zero, while the small subset of non-zero weights defines the discovered model. Unlike classical network weights, these weights are physically interpretable and translate naturally into engineering parameters and microstructural features such as stiffness and fiber orientation. Our results suggest that Constitutive Artificial Neural Networks enable automated model, parameter, and experiment discovery and could initiate a paradigm shift in constitutive modeling, from user-defined to automated model selection and parameterization.

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Section: Constitutive Modelingmentioning

confidence: 99%

Automated model discovery for skin: Discovering the best model, data, and experiment

Linka

Tepole

Holzapfel

et al. 2022

Preprint

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show abstract

“…At this point, we could use an arbitrary neural network to learn the functional relation between P and F and many neural networks in the literature do exactly that [23, 40, 55]. However, the functions P ( F ) that we learn through this approach generally violate widely-accepted thermodynamical constraints and their parameters have no physical meaning [24].…”

Section: Methodsmentioning

confidence: 99%

Automated model discovery for human brain using Constitutive Artificial Neural Networks

Linka

Pierre

Kuhl

2022

Preprint

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The brain is our softest and most vulnerable organ, and understanding its physics is a challenging but significant task. Massive efforts have been dedicated at testing the human brain, and various competing models have emerged to characterize its response to mechanical loading. However, selecting the best constitutive model remains a heuristic process that strongly depends on user experience and personal preference. Here we challenge the conventional wisdom to first select a constitutive model and then fit its parameters to experimental data. Instead, we propose a new strategy that simultaneously discovers both model and parameters that best describe the data. Towards this goal, we integrate more than a century of knowledge in thermodynamics and state-of-the-art machine learning to build a family of Constitutive Artificial Neural Networks that enable automated model discovery for human brain tissue. Our overall design paradigm is to reverse engineer a Constitutive Artificial Neural Network from a set of functional building blocks that are, by design, a generalization of widely used and commonly accepted constitutive models, including the neo Hooke, Blatz Ko, Mooney Rivlin, Demiray, Gent, and Holzapfel models. By constraining the input, output, activation functions, and architecture, our network a priori satisfies thermodynamic consistency, material objectivity, material symmetry, physical constrains, and polyconvexity. We demonstrate that our network autonomously discovers both model and parameters that best characterize the behavior of human gray and white matter under tension, compression, and shear. Importantly, our network weights translate naturally into physically meaningful material parameters, e.g., shear moduli of 1.82kPa, 0.88kPa, 0.94kPa, and 0.54kPa for the cortex, basal ganglia, corona radiata, and corpus callosum. Our results suggest that Constitutive Artificial Neural Networks have the potential to induce a paradigm shift in soft tissue modeling, from user-defined model selection to automated model discovery. Our source code, data, and examples are available at https://github.com/LivingMatterLab/CANN.

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“…A subsequent optimization with the high fidelity model can mitigate these drawbacks and increase the accuracy of the final identified parameters. Schulte et al (2023) used a neural network to obtain first estimates for a mechanical characterization task and subsequently continued the optimization with a high fidelity finite element model.…”

Section: Introductionmentioning

confidence: 99%

Using dropout based active learning and surrogate models in the inverse viscoelastic parameter identification of human brain tissue

Hinrichsen,

Ferlay,

Reiter

et al. 2024

Front. Physiol.

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Inverse mechanical parameter identification enables the characterization of ultrasoft materials, for which it is difficult to achieve homogeneous deformation states. However, this usually involves high computational costs that are mainly determined by the complexity of the forward model. While simulation methods like finite element models can capture nearly arbitrary geometries and implement involved constitutive equations, they are also computationally expensive. Machine learning models, such as neural networks, can help mitigate this problem when they are used as surrogate models replacing the complex high fidelity models. Thereby, they serve as a reduced order model after an initial training phase, where they learn the relation of in- and outputs of the high fidelity model. The generation of the required training data is computationally expensive due to the necessary simulation runs. Here, active learning techniques enable the selection of the “most rewarding” training points in terms of estimated gained accuracy for the trained model. In this work, we present a recurrent neural network that can well approximate the output of a viscoelastic finite element simulation while significantly speeding up the evaluation times. Additionally, we use Monte-Carlo dropout based active learning to identify highly informative training data. Finally, we showcase the potential of the developed pipeline by identifying viscoelastic material parameters for human brain tissue.

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Machine learning-assisted parameter identification for constitutive models based on concatenated loading path sequences

Cited by 24 publications

References 35 publications

Automated model discovery for skin: Discovering the best model, data, and experiment

Automated model discovery for skin: Discovering the best model, data, and experiment

Automated model discovery for human brain using Constitutive Artificial Neural Networks

Using dropout based active learning and surrogate models in the inverse viscoelastic parameter identification of human brain tissue

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