Immersed boundary parametrizations for full waveform inversion

Bürchner, Tim; Kopp, Philipp; Kollmannsberger, Stefan; Rank, Ernst

doi:10.1016/j.cma.2023.115893

Cited by 12 publications

(22 citation statements)

References 43 publications

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“…To this end, an additional weight, i.e. coefficient clipping is used, where the absolute value is clipped to the range of a small value close to zero and an upper bound one or slightly exceeding one [37].…”

Section: Adjoint Methodsmentioning

confidence: 99%

“…In the continuous adjoint method, the gradient is derived analytically before its discretization, as e.g. derived in [37]. This third modification has transformed the approach into the classical full waveform inversion based on finite differences.…”

Section: Adjoint Methodsmentioning

confidence: 99%

“…These originate in the computation of the Fréchet kernel used to compute the gradient ∇ γ L M via the integration of K γ over the spatial and time domains (c.f. [37] for more details). To compute equation ( 25), the temporal and spatial gradients of the solution field u and the adjoint field u † are computed with finite differences.…”

Section: Adjoint Methodsmentioning

confidence: 99%

“…In case of multiple sources, an average of the mean squared errors L M and their gradients ∇ m L M must be considered in the iteration update from equation (10). More details on the computation of the gradient using the adjoint method are found in [37]. For a more in depth explanation of the adjoint method for inverse problems, see Givoli [33].…”

Section: Full Waveform Inversionmentioning

confidence: 99%

“…The two-dimensional case is strongly inspired by [37], where a circular hole with a diameter of 5 mm is to be detected on a 100 mm × 50 mm rectangular plate, illustrated in figure 7a. We do not provide specific information about the hole to the machine learning algorithms, which implies the entire material distribution γ(x) has to be estimated.…”

Section: Two-dimensional Casementioning

confidence: 99%

See 4 more Smart Citations

On the Use of Neural Networks for Full Waveform Inversion

Herrmann¹,

Bürchner²,

Dietrich³

et al. 2023

Preprint

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Neural networks have recently gained attention in solving inverse problems. One prominent methodology are Physics-Informed Neural Networks (PINNs) which can solve both forward and inverse problems. In the paper at hand, full waveform inversion is the considered inverse problem. The performance of PINNs is compared against classical adjoint optimization, focusing on three key aspects: the forward-solver, the neural network Ansatz for the inverse field, and the sensitivity computation for the gradient-based minimization. Starting from PINNs, each of these key aspects is adapted individually until the classical adjoint optimization emerges. It is shown that it is beneficial to use the neural network only for the discretization of the unknown material field, where the neural network produces reconstructions without oscillatory artifacts as typically encountered in classical full waveform inversion approaches. Due to this finding, a hybrid approach is proposed. It exploits both the efficient gradient computation with the continuous adjoint method as well as the neural network Ansatz for the unknown material field. This new hybrid approach outperforms Physics-Informed Neural Networks and the classical adjoint optimization in settings of two and three-dimensional examples.

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Section: Adjoint Methodsmentioning

confidence: 99%

Section: Adjoint Methodsmentioning

confidence: 99%

Section: Adjoint Methodsmentioning

confidence: 99%

Section: Full Waveform Inversionmentioning

confidence: 99%

Section: Two-dimensional Casementioning

confidence: 99%

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On the Use of Neural Networks for Full Waveform Inversion

Herrmann¹,

Bürchner²,

Dietrich³

et al. 2023

Preprint

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Single‐field identification of inclusions and cavities in an elastic medium

Rabinovich,

Givoli,

Turkel

2023

Numerical Meth Engineering

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The inverse problem of identifying a small unknown inclusion or cavity in an elastic medium is considered. Important applications are structural damage identification, medical imaging and geophysical exploration; the latter is the focus of the present investigation. It is assumed that the (isotropic but possibly heterogeneous) material properties of the medium are known, except for the presence of a small inclusion of a different material or of a small cavity. The goal is to find the location, size and shape of the inclusion or cavity. Identification is performed using full waveform inversion (FWI) and the adjoint method for the efficient calculation of the gradient of the misfit function. The identification is accomplished by considering a single unknown material‐property field. The inclusion manifests itself in the inverse solution as a local region where the unknown material property becomes significantly different than the known background property. The limiting case of cavity identification requires special treatment in the minimization process to avoid failure, as Bürchner et al. showed empirically for the scalar wave equation. Their ‐scaling approach, whose success is explained mathematically here for the first time, is extended to elastodynamics. The performance of the proposed method is demonstrated via numerical examples, involving two geophysical models: a homogeneous model and the heterogeneous Marmousi model, which is a standard testing model in geophysical research.

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An automatic simulation pipeline for coupled simulations of acoustic damping materials

Radtke,

Marter,

Eisenträger

et al. 2024

Proc Appl Math and Mech

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Foamed materials are widely used to reduce noise due to their comparably good acoustic damping behavior. However, out of a large variety of these materials a suitable candidate has to be identified for each application. This is a challenging process that is typically guided by experiments and experience. While numerical simulations could support these experiments and reduce the effort to a great extent, no suitable discretization approach has yet been established that can fully capture the complex geometry of the foam. A fully resolved model is desirable in order to yield reliable predictions that can then be used to establish homogenized models. We established a monolithic coupling approach based on the finite cell method (FCM) that realizes a vibroacoustic simulation in this sense. The fluid and the structure domain are discretized by Cartesian grids and the geometry defined based on computed tomography scans is accounted for during the quadrature of the weak form. Our simulation in the time domain makes use of explicit time marching schemes and is therefore limited by a critical time step size. This is known to be arbitrarily low for discretizations with the FCM containing cells with arbitrarily small support. As a remedy against this we use the classical ‐stabilization technique and investigate its potentials and limitations.

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Immersed boundary parametrizations for full waveform inversion

Cited by 12 publications

References 43 publications

On the Use of Neural Networks for Full Waveform Inversion

On the Use of Neural Networks for Full Waveform Inversion

Single‐field identification of inclusions and cavities in an elastic medium

An automatic simulation pipeline for coupled simulations of acoustic damping materials

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