Learning hidden elasticity with deep neural networks

Chen, Chun-Teh; Gu, Grace X.

doi:10.1073/pnas.2102721118

Cited by 46 publications

(13 citation statements)

References 49 publications

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“…Moreover, it would allow us to create descriptive computational models to investigate cell biomechanics, including the potential to estimate cell elasticity and identify loading modalities that lead to cell softening and stiffening. 59 Taken together, these experimental and computational approaches would inform our understanding of AF cell mechanobiology and potentially identify the initiation and development of disc degeneration. Future work will investigate the response of human AF cells within the device as well as 3D cell-laden constructs.…”

Section: Discussionmentioning

confidence: 99%

Design of a flexing organ-chip to model in situ loading of the intervertebral disc

et al. 2022

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The leading cause of disability of all ages worldwide is severe lower back pain. To address this untreated epidemic, further investigation is needed into the leading cause of back pain, intervertebral disc degeneration. In particular, microphysiological systems modeling critical tissues in a degenerative disc, like the annulus fibrosus (AF), are needed to investigate the effects of complex multiaxial strains on AF cells. By replicating these mechanobiological effects unique to the AF that are not yet understood, we can advance therapies for early-stage degeneration at the cellular level. To this end, we designed, fabricated, and collected proof-of-concept data for a novel microphysiological device called the flexing annulus-on-a-chip (AoC). We used computational models and experimental measurements to characterize the device’s ability to mimic complex physiologically relevant strains. As a result, these strains proved to be controllable, multi-directional, and uniformly distributed with magnitudes ranging from [Formula: see text]% to 12% in the axial, radial, and circumferential directions, which differ greatly from applied strains possible in uniaxial devices. Furthermore, after withstanding accelerated life testing (66 K cycles of 10% strain) and maintaining 2000 bovine AF cells without loading for more than three weeks the AoC proved capable of long-term cell culture. Additionally, after strain (3.5% strain for 75 cycles at 0.5 Hz) was applied to a monolayer of AF cells in the AoC, a population remained adhered to the channel with spread morphology. The AoC can also be tailored for other annular structures in the body such as cardiovascular vessels, lymphatic vessels, and the cervix.

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Section: Discussionmentioning

confidence: 99%

Design of a flexing organ-chip to model in situ loading of the intervertebral disc

et al. 2022

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“…Recent advances in laser-based ultrasonic testing has led to the emergence of dense spatiotemporal datasets which along with suitable data analytic solutions may lead to better understanding of the mechanics of complex materials and components. This includes learning of distributed mechanical properties from test data which is of interest in a wide spectrum of applications from medical diagnosis to additive manufacturing [1,2,3,4,5,6,7]. This work makes use of recent progress in deep learning [8,9] germane to direct and inverse problems in partial differential equations [10,11,12,13] to develop a systematic full-field inversion framework to recover the profile of pertinent physical quantities in layered components from laser ultrasonic measurements.…”

Section: Introductionmentioning

confidence: 99%

Deep learning for full-field ultrasonic characterization

Xu¹,

Pourahmadian²,

Song³

et al. 2023

Preprint

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This study takes advantage of recent advances in machine learning to establish a physics-based data analytic platform for distributed reconstruction of mechanical properties in layered components from full waveform data. In this vein, two logics, namely the direct inversion and physics-informed neural networks (PINNs), are explored. The direct inversion entails three steps: (i) spectral denoising and differentiation of the full-field data, (ii) building appropriate neural maps to approximate the profile of unknown physical and regularization parameters on their respective domains, and (iii) simultaneous training of the neural networks by minimizing the Tikhonov-regularized PDE loss using data from (i). PINNs furnish efficient surrogate models of complex systems with predictive capabilities via multitask learning where the field variables are modeled by neural maps endowed with (scaler or distributed) auxiliary parameters such as physical unknowns and loss function weights. PINNs are then trained by minimizing a measure of data misfit subject to the underlying physical laws as constraints. In this study, to facilitate learning from ultrasonic data, the PINNs loss adopts (a) wavenumber-dependent Sobolev norms to compute the data misfit, and (b) non-adaptive weights in a specific scaling framework to naturally balance the loss objectives by leveraging the form of PDEs germane to elasticwave propagation. Both paradigms are examined via synthetic and laboratory test data. In the latter case, the reconstructions are performed at multiple frequencies and the results are verified by a set of complementary experiments highlighting the importance of verification and validation in data-driven modeling.

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“…In the model-free data-driven realm, recent works (Leygue et al, 2018;Dalémat et al, 2019;Cameron and Tasan, 2021) have demonstrated estimation of stress fields from full-field displacement data. In the model-based realm, physics-informed neural networks (PINNs) and their variations have shown promising results -by first learning the forward solution, i.e., displacement fields, to the mechanical boundary boundary value problem as a function of the material parameters and then estimating the unknown parameters via gradient-based optimization (Huang et al, 2020;Tartakovsky et al, 2018;Haghighat et al, 2020;Chen and Gu, 2021). However, all the aforementioned methods (including FEMU, VFM, and PINNs) are limited to a priori assumed constitutive models (e.g., with known deformation modes) with only a few unknown parameters.…”

Section: Introductionmentioning

confidence: 99%

Bayesian-EUCLID: discovering hyperelastic material laws with uncertainties

Joshi,

Thakolkaran,

Zheng

et al. 2022

Preprint

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Within the scope of our recent approach for Efficient Unsupervised Constitutive Law Identification and Discovery (EUCLID), we propose an unsupervised Bayesian learning framework for discovery of parsimonious and interpretable constitutive laws with quantifiable uncertainties. As in deterministic EUCLID, we do not resort to stress data, but only to realistically measurable full-field displacement and global reaction force data; as opposed to calibration of an a priori assumed model, we start with a constitutive model ansatz based on a large catalog of candidate functional features; we leverage domain knowledge by including features based on existing, both physics-based and phenomenological, constitutive models. In the new Bayesian-EUCLID approach, we use a hierarchical Bayesian model with sparsitypromoting priors and Monte Carlo sampling to efficiently solve the parsimonious model selection task and discover physically consistent constitutive equations in the form of multivariate multi-modal probabilistic distributions. We demonstrate the ability to accurately and efficiently recover isotropic and anisotropic hyperelastic models like the Neo-Hookean, Isihara, Gent-Thomas, Arruda-Boyce, Ogden, and Holzapfel models in both elastostatics and elastodynamics. The discovered constitutive models are reliable under both epistemic uncertainties -i.e. uncertainties on the true features of the constitutive catalog -and aleatoric uncertainties -which arise from the noise in the displacement field data, and are automatically estimated by the hierarchical Bayesian model.

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Learning hidden elasticity with deep neural networks

Cited by 46 publications

References 49 publications

Design of a flexing organ-chip to model in situ loading of the intervertebral disc

Design of a flexing organ-chip to model in situ loading of the intervertebral disc

Deep learning for full-field ultrasonic characterization

Bayesian-EUCLID: discovering hyperelastic material laws with uncertainties

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