On the use of neural networks for full waveform inversion

Herrmann, Leon; Bürchner, Tim; Dietrich, Felix; Kollmannsberger, Stefan

doi:10.1016/j.cma.2023.116278

Cited by 6 publications

(7 citation statements)

References 66 publications

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“…This has, for example, been shown for the identification of material properties [285,[309][310][311][312]. By contrast, for inverse problems with only partial knowledge, the applicability of PINNs is limited [313], as both forward and inverse solution have to be learned simultaneously. Most applications therefore limit themselves to simpler inversions such as size and shape optimization.…”

Section: Applications To Forward Problemsmentioning

confidence: 99%

“…Secondly, the gradient computation is simplified, as automatic differentiation through the forward operator F is straightforward in contrast to the adjoint state method [452,453]. Note however, that for time-stepping procedures, the computational cost might be greater for automatic differentiation, as shown in [313]. Applications include full waveform inversion [313], topology optimization [454][455][456], and control problems [70,72,444].…”

Section: Optimizationmentioning

confidence: 99%

“…Note however, that for time-stepping procedures, the computational cost might be greater for automatic differentiation, as shown in [313]. Applications include full waveform inversion [313], topology optimization [454][455][456], and control problems [70,72,444].…”

Section: Optimizationmentioning

confidence: 99%

“…Another option of introducing NNs to the optimization loop is to use NNs as an ansatz of λ, see, e.g., [313,444,[466][467][468][469][470][471][472][473][474]. In the context of inverse problems [313,444,[466][467][468][469][470], the NN acts as regularizer on a spatially varying inverse quantity λ(x) = I N N (x; θ ), providing both smoother and sharper solutions. For topology optimization with a NN parametrization of the density function [471][472][473][474], no regularizing effect was observed.…”

Section: Optimizationmentioning

confidence: 99%

“…Extensions using specialized NN architectures for implicit representations [475][476][477][478][479][480] have been presented in the context of topology optimization in [481]. Furthermore, [313,468,472] showed how to conduct the gradient computation without automatic differentiation through the solver F. The gradient computation is split up via the chain rule:…”

Section: Optimizationmentioning

confidence: 99%

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Deep learning in computational mechanics: a review

Herrmann,

Kollmannsberger

2024

Comput Mech

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The rapid growth of deep learning research, including within the field of computational mechanics, has resulted in an extensive and diverse body of literature. To help researchers identify key concepts and promising methodologies within this field, we provide an overview of deep learning in deterministic computational mechanics. Five main categories are identified and explored: simulation substitution, simulation enhancement, discretizations as neural networks, generative approaches, and deep reinforcement learning. This review focuses on deep learning methods rather than applications for computational mechanics, thereby enabling researchers to explore this field more effectively. As such, the review is not necessarily aimed at researchers with extensive knowledge of deep learning—instead, the primary audience is researchers on the verge of entering this field or those attempting to gain an overview of deep learning in computational mechanics. The discussed concepts are, therefore, explained as simple as possible.

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Section: Applications To Forward Problemsmentioning

confidence: 99%

Section: Optimizationmentioning

confidence: 99%

Section: Optimizationmentioning

confidence: 99%

Section: Optimizationmentioning

confidence: 99%

Section: Optimizationmentioning

confidence: 99%

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Deep learning in computational mechanics: a review

Herrmann,

Kollmannsberger

2024

Comput Mech

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On neural networks for generating better local optima in topology optimization

Herrmann,

Sigmund,

et al. 2024

Struct Multidisc Optim

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Neural networks have recently been employed as material discretizations within adjoint optimization frameworks for inverse problems and topology optimization. While advantageous regularization effects and better optima have been found for some inverse problems, the benefit for topology optimization has been limited—where the focus of investigations has been the compliance problem. We demonstrate how neural network material discretizations can, under certain conditions, find better local optima in more challenging optimization problems, where we here specifically consider acoustic topology optimization. The chances of identifying a better optimum can significantly be improved by running multiple partial optimizations with different neural network initializations. Furthermore, we show that the neural network material discretization’s advantage comes from the interplay with the Adam optimizer and emphasize its current limitations when competing with constrained and higher-order optimization techniques. At the moment, this discretization has only been shown to be beneficial for unconstrained first-order optimization.

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