A full-field image conversion method for the inverse conductivity problem with internal measurements

Bellis, Cédric; Moulinec, Hervé

doi:10.1098/rspa.2015.0488

Cited by 7 publications

(11 citation statements)

References 30 publications

(40 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The first approach, aimed at reconstructing an isotropic conductivity, uses power densities associated with 3 conductivity solutions, and solves a local dynamical system for a quaternionvalued function, followed by a Poisson problem for the conductivity σ. Note that one could also solve for σ by integrating (17) along curves, though the Poisson equation (18) presents the advantage of projecting out the curl part of the right-hand-side of (17) before resolution.…”

Section: Discussionmentioning

confidence: 99%

Imaging of isotropic and anisotropic conductivities from power densities in three dimensions

Monard

Rim

2018

Inverse Problems

View full text Add to dashboard Cite

We present numerical reconstructions of anisotropic conductivity tensors in three dimensions, from knowledge of a finite family of power density functionals. Such a problem arises in the coupled-physics imaging modality Ultrasound Modulated Electrical Impedance Tomography for instance. We improve on the algorithms previously derived in [9,32] for both isotropic and anisotropic cases, and we address the well-known issue of vanishing determinants in particular. The algorithm is implemented and we provide numerical results that illustrate the improvements. 1 γ is uniformly elliptic if there exists a constant κ ≥ 1 such that κ −1 |ξ| 2 ≤ γ(x)ξ · ξ ≤ κ|ξ| 2 for every x ∈ X and ξ ∈ R 3 .

show abstract

Section: Discussionmentioning

confidence: 99%

Imaging of isotropic and anisotropic conductivities from power densities in three dimensions

Monard

Rim

2018

Inverse Problems

View full text Add to dashboard Cite

show abstract

“…A coupling to the Nemat-Nasser-Iwakuma-Hejazi estimates for conductivity was proposed [202], and the conductivity of polygonal aggregates [203] was addressed. Also, FFT-based methods were applied to compute the through-thickness conductivity of heterogeneous plates [204] and for an inverse reconstruction of the local conductivity [205]. Furthermore, extensions to compute Fickian diffusion [206] and ionic conductivity [207] were reported, as were applications to the effective conductivity and diffusivity of porous carbon electrodes [208], the electronic conductivity of lithium ion positive electrodes [209] and the conductivity of solid oxide fuel cell anodes [210].…”

Section: Conductivity and Diffusivitymentioning

confidence: 99%

A review of nonlinear FFT-based computational homogenization methods

Schneider

2021

Acta Mech

150

View full text Add to dashboard Cite

Since their inception, computational homogenization methods based on the fast Fourier transform (FFT) have grown in popularity, establishing themselves as a powerful tool applicable to complex, digitized microstructures. At the same time, the understanding of the underlying principles has grown, in terms of both discretization schemes and solution methods, leading to improvements of the original approach and extending the applications. This article provides a condensed overview of results scattered throughout the literature and guides the reader to the current state of the art in nonlinear computational homogenization methods using the fast Fourier transform.

show abstract

“…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

View full text Add to dashboard Cite

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.

show abstract

A full-field image conversion method for the inverse conductivity problem with internal measurements

Cited by 7 publications

References 30 publications

Imaging of isotropic and anisotropic conductivities from power densities in three dimensions

Imaging of isotropic and anisotropic conductivities from power densities in three dimensions

A review of nonlinear FFT-based computational homogenization methods

Deep learning for full-field ultrasonic characterization

Contact Info

Product

Resources

About