Manifold learning based data-driven modeling for soft biological tissues

He, Qi; Laurence, Devin W.; Lee, Chung‐Hao; Chen, Jiun‐Shyan

doi:10.1016/j.jbiomech.2020.110124

Cited by 36 publications

(22 citation statements)

References 43 publications

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“…This setting corresponds to a scenario that different lab tests are available for a given material sample with unknown microstructure, and our learning goal is to predict the mechanical response of this sample under a new and unseen loading. We note that this setting reflects the typical material mechanical testing experiments, see, e.g., [28], where one representative material sample is tested under several loading protocols and the responses, such as the displacement fields and/or stretch-stress curves, are provided. Setting and results of porous medium I.…”

Section: The Flow Through a Porous Mediummentioning

confidence: 99%

“…To mimic the real-world mechanical test settings (see, e.g. [28]), we generated 9 different biaxial loading protocol sets as listed in Table 5, with 100 samples for each set. For each sample, a uniform uniaxial displacement boundary condition u D = (U x , 0) was applied on the right edge of the plate, and another uniform uniaxial displacement u D = (0, U y ) was prescribed on the top edge.…”

Section: The Deformation Of a Hyperelastic And Anisotropic Fiber-rein...mentioning

confidence: 99%

“…To address these challenges, data-driven computing has been considered as an alternative to the conventional constitutive modeling. In recent years, there has been significant progress in the development of deep neural networks (NNs), focusing on learning the hidden physics of a complex system [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35]. Among these works, several studies that use neural networks in modeling heterogeneous materials have been conducted [36][37][38][39][40][41].…”

Section: Introductionmentioning

confidence: 99%

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Learning Deep Implicit Fourier Neural Operators (IFNOs) with Applications to Heterogeneous Material Modeling

You,

Zhang,

Ross

et al. 2022

Preprint

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Constitutive modeling based on continuum mechanics theory has been a classical approach for modeling the mechanical responses of materials. However, when constitutive laws are unknown or when defects and/or high degrees of heterogeneity are present, these classical models may become inaccurate. In this work, we propose to use data-driven modeling, which directly utilizes high-fidelity simulation and/or experimental measurements to predict a material's response without using conventional constitutive models. Specifically, the material response is modeled by learning the implicit mappings between loading conditions and the resultant displacement and/or damage fields, with the neural network serving as a surrogate for a solution operator. To model the complex responses due to material heterogeneity and defects, we develop a novel deep neural operator architecture, which we coin as the Implicit Fourier Neural Operator (IFNO). In the IFNO, the increment between layers is modeled as an integral operator to capture the long-range dependencies in the feature space. As the network gets deeper, the limit of IFNO becomes a fixed point equation that yields an implicit neural operator and naturally mimics the displacement/damage fields solving procedure in material modeling problems. To obtain an efficient implementation, we parameterize the integral kernel of this integral operator directly in the Fourier space and interpret the network as discretized integral (nonlocal) differential equations, which consequently allow for the fast Fourier transformation (FFT) and accelerated learning techniques for deep networks. We demonstrate the performance of our proposed method for a number of examples, including hyperelastic, anisotropic and brittle materials. As an application, we further employ the proposed approach to learn the material models directly from digital image correlation (DIC) tracking measurements, and show that the learned solution operators substantially outperform the conventional constitutive models in predicting displacement fields.

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Section: The Flow Through a Porous Mediummentioning

confidence: 99%

Section: The Deformation Of a Hyperelastic And Anisotropic Fiber-rein...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Learning Deep Implicit Fourier Neural Operators (IFNOs) with Applications to Heterogeneous Material Modeling

You,

Zhang,

Ross

et al. 2022

Preprint

Self Cite

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“…Such flexibility allows a computational model to capture certain information that is hard to identify by conventional approaches. For example, 17 introduced the deep autoencoder to discover the latent low-dimensional data pattern embedded in noisy material datasets, which significantly enhanced the effectiveness of the physics-constrained data-driven approach developed by He and Chen (2020) 18 and He et al (2021) 19 . Lee and Carlberg (2020) 20 proposed a model order reduction technique based on low-dimensional nonlinear manifolds constructed by the deep convolutional autoencoder and demonstrated the enhanced performance over linear subspace-based reduced order modeling techniques.…”

Section: Introductionmentioning

confidence: 99%

A neural network‐enhanced reproducing kernel particle method for modeling strain localization

Baek

Chen

Susuki

2022

Numerical Meth Engineering

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Modeling the localized intensive deformation in a damaged solid requires highly refined discretization for accurate prediction, which significantly increases the computational cost.Although adaptive model refinement can be employed for enhanced effectiveness, it is cumbersome for the traditional mesh-based methods to perform while modeling the evolving localizations. In this work, neural network-enhanced reproducing kernel particle method (NN-RKPM) is proposed, where the location, orientation, and shape of the solution transition near a localization is automatically captured by the NN approximation via a block-level neural network optimization. The weights and biases in the blocked parametrization network control the location and orientation of the localization. The designed basic four-kernel NN block is capable of capturing a triple junction or a quadruple junction topological pattern, while more complicated localization topological patters are captured by the superposition of multiple fourkernel NN blocks. The standard RK approximation is then utilized to approximate the smooth part of the solution, which permits a much coarser discretization than the high-resolution discretization needed to capture sharp solution transitions with the conventional methods. A regularization of the neural network approximation is additionally introduced for discretizationindependent material responses. The effectiveness of the proposed NN-RKPM is verified by a series of numerical verifications.

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“…However, limited data and functional form assumptions inevitably introduce errors to the model parameter calibration and model prediction. Moreover, with the pre-defined functions, constitutive laws often lack generality to capture full aspects of material behaviors [1,2].…”

Section: Introductionmentioning

confidence: 99%

Thermodynamically Consistent Machine-Learned Internal State Variable Approach for Data-Driven Modeling of Path-Dependent Materials

He,

Chen

2022

Preprint

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Characterization and modeling of path-dependent behaviors of complex materials by phenomenological models remains challenging due to difficulties in formulating mathematical expressions and internal state variables (ISVs) governing path-dependent behaviors. Data-driven machine learning models, such as deep neural networks and recurrent neural networks (RNNs), have become viable alternatives. However, pure black-box data-driven models mapping inputs to outputs without considering the underlying physics suffer from unstable and inaccurate generalization performance. This study proposes a machinelearned physics-informed data-driven constitutive modeling approach for pathdependent materials based on the measurable material states. The proposed data-driven constitutive model is designed with the consideration of universal thermodynamics principles, where the ISVs essential to the material pathdependency are inferred automatically from the hidden state of RNNs. The RNN describing the evolution of the data-driven machine-learned ISVs follows the thermodynamics second law. To enhance the robustness and accuracy of RNN models, stochasticity is introduced to model training. The effects of the number of RNN history steps, the internal state dimension, the model complexity, and the strain increment on model performances have been investigated. The effectiveness of the proposed method is evaluated by modeling soil material behaviors under cyclic shear loading using experimental stress-strain data.

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Manifold learning based data-driven modeling for soft biological tissues

Cited by 36 publications

References 43 publications

Learning Deep Implicit Fourier Neural Operators (IFNOs) with Applications to Heterogeneous Material Modeling

Learning Deep Implicit Fourier Neural Operators (IFNOs) with Applications to Heterogeneous Material Modeling

A neural network‐enhanced reproducing kernel particle method for modeling strain localization

Thermodynamically Consistent Machine-Learned Internal State Variable Approach for Data-Driven Modeling of Path-Dependent Materials

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