Physics informed neural networks for continuum micromechanics

Henkes, Alexander; Wessels, Henning; Mahnken, Rolf

doi:10.1016/j.cma.2022.114790

Cited by 125 publications

(46 citation statements)

References 27 publications

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“…These values can be translated to the material parameters λ and µ given in Eq. ( 13) in the well known way, see e.g., [57]. The microstructure is illustrated in Figure 2.…”

Section: Example 1: Spherical Inclusionsmentioning

confidence: 90%

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Three-dimensional microstructure generation using generative adversarial neural networks in the context of continuum micromechanics

Henkes,

Wessels

2022

Preprint

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Multiscale simulations are demanding in terms of computational resources. In the context of continuum micromechanics, the multiscale problem arises from the need of inferring macroscopic material parameters from the microscale. If the underlying microstructure is explicitly given by means of µCT-scans, convolutional neural networks can be used to learn the microstructure-property mapping, which is usually obtained from computational homogenization. The CNN approach provides a significant speedup, especially in the context of heterogeneous or functionally graded materials. Another application is uncertainty quantification, where many expansive evaluations are required. However, one bottleneck of this approach is the large number of training microstructures needed.This work closes this gap by proposing a generative adversarial network tailored towards three-dimensional microstructure generation. The lightweight algorithm is able to learn the underlying properties of the material from a single µCT-scan without the need of explicit descriptors. During prediction time, the network can produce unique three-dimensional microstructures with the same properties of the original data in a fraction of seconds and at consistently high quality.

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“…These values can be translated to the material parameters λ and µ given in Eq. ( 13) in the well known way, see e.g., [57]. The microstructure is illustrated in Figure 2.…”

Section: Example 1: Spherical Inclusionsmentioning

confidence: 90%

“…As it was shown in [57] and [78], physical constraints can be introduced to ANN in the context of continuum mechanics, which enable the network to solve the underlying partial differential equations directly, without the need of training data. This approach is commonly known as physics informed neural networks.…”

Section: Data Availabilitymentioning

confidence: 99%

Three-dimensional microstructure generation using generative adversarial neural networks in the context of continuum micromechanics

Henkes,

Wessels

2022

Preprint

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“…Machine learning methods are rapidly developing as an alternative to traditional approaches to overcome the issues mentioned above. Machine learning methods can be classified as data-driven models [6][7][8][9][10][11][12][13][14][15][16] and physics-informed neural networks (PINNs) [17][18][19][20][21][22][23][24] . In data-driven models, data from experimental and computational results are used to train the models.…”

Section: Introductionmentioning

confidence: 99%

Optimizing Hyperparameters and Architecture of Deep Energy Method

Chadha¹,

Abueidda²,

Korić³

et al. 2022

Preprint

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The deep energy method (DEM) employs the principle of minimum potential energy to train neural network models to predict displacement at a state of equilibrium under given boundary conditions. The accuracy of the model is contingent upon choosing appropriate hyperparameters. The hyperparameters have traditionally been chosen based on literature or through manual iterations. The displacements predicted using hyperparameters suggested in the literature do not ensure the minimum potential energy of the system. Additionally, they do not necessarily generalize to different load cases. Selecting hyperparameters through manual trial and error and grid search algorithms can be highly time-consuming. We propose a systematic approach using the Bayesian optimization algorithms and random search to identify optimal values for these parameters. Seven hyperparameters are optimized to obtain the minimum potential energy of the system under compression, tension, and bending loads cases. In addition to Bayesian optimization, Fourier feature mapping is also introduced to improve accuracy. The models trained using optimal hyperparameters and Fourier feature mapping could accurately predict deflections compared to finite element analysis for linear elastic materials. The deflections obtained for tension and compression load cases are found to be more sensitive to values of hyperparameters compared to bending. The approach can be easily extended to 3D and other material models.

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“…PINNs have been utilized in different ways. For example, one approach in which PINNs are used is to define the loss function as the PDEs' residual at specific collocation points in the physical domain and on its corresponding boundary and initial conditions [19,20,21]. This approach is commonly called the deep collocation method (DCM).…”

Section: Introductionmentioning

confidence: 99%

Enhanced physics-informed neural networks for hyperelasticity

Abueidda¹,

Korić²,

Guleryuz³

et al. 2022

Preprint

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Physics-informed neural networks have gained growing interest. Specifically, they are used to solve partial differential equations governing several physical phenomena. However, physics-informed neural network models suffer from several issues and can fail to provide accurate solutions in many scenarios. We discuss a few of these challenges and the techniques, such as the use of Fourier transform, that can be used to resolve these issues. This paper proposes and develops a physicsinformed neural network model that combines the residuals of the strong form and the potential energy, yielding many loss terms contributing to the definition of the loss function to be minimized. Hence, we propose using the coefficient of variation weighting scheme to dynamically and adaptively assign the weight for each loss term in the loss function. The developed PINN model is standalone and meshfree. In other words, it can accurately capture the mechanical response without requiring any labeled data. Although the framework can be used for many solid mechanics problems, we focus on three-dimensional (3D) hyperelasticity, where we consider two hyperelastic models. Once the model is trained, the response can be obtained almost instantly at any point in the physical domain, given its spatial coordinates. We demonstrate the framework's performance by solving different problems with various boundary conditions. KeywordsComputational mechanics • Curriculum learning • Fourier transform • Meshfree method • Multi-loss weighting • Partial differential equations Recently, rapid growth in the utilization of deep learning (DL) and data-driven modeling has been seen in computational solid mechanics [4

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Physics informed neural networks for continuum micromechanics

Cited by 125 publications

References 27 publications

Three-dimensional microstructure generation using generative adversarial neural networks in the context of continuum micromechanics

Three-dimensional microstructure generation using generative adversarial neural networks in the context of continuum micromechanics

Optimizing Hyperparameters and Architecture of Deep Energy Method

Enhanced physics-informed neural networks for hyperelasticity

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