Physics-guided deep learning using Fourier neural operators for solving the acoustic VTI wave equation

Konuk, Tugrul; Shragge, Jeffrey

doi:10.3997/2214-4609.202113304

Cited by 14 publications

(3 citation statements)

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“…Motivated by physics-informed DeepONet (PI-DeepONet) proposed in [27] and [26], the physics-informed FNO (PINO) was proposed in [33,34] as an integration of operator learning and physics-informed settings. PINO reduces the labelled dataset requirement for training the neural operator and helps in faster convergence of the solution.…”

Section: Physics-informed Fnomentioning

confidence: 99%

Physics-Informed Deep Neural Operator Networks

Goswami¹,

Bora²,

Yu³

et al. 2022

Preprint

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Standard neural networks can approximate general nonlinear operators, represented either explicitly by a combination of mathematical operators, e.g., in an advection-diffusion-reaction partial differential equation, or simply as a black box, e.g., a system-of-systems. The first neural operator was the Deep Operator Network (DeepONet), proposed in 2019 based on rigorous approximation theory. Since then, a few other less general operators have been published, e.g., based on graph neural networks or Fourier transforms. For black box systems, training of neural operators is data-driven only but if the governing equations are known they can be incorporated into the loss function during training to develop physics-informed neural operators. Neural operators can be used as surrogates in design problems, uncertainty quantification, autonomous systems, and almost in any application requiring real-time inference. Moreover, independently pre-trained DeepONets can be used as components of a complex multi-physics system by coupling them together with relatively light training. Here, we present a review of DeepONet, the Fourier neural operator, and the graph neural operator, as well as appropriate extensions with feature expansions, and highlight their usefulness in diverse applications in computational mechanics, including porous media, fluid mechanics, and solid mechanics.

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Section: Physics-informed Fnomentioning

confidence: 99%

Physics-Informed Deep Neural Operator Networks

Goswami¹,

Bora²,

Yu³

et al. 2022

Preprint

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“…In light of their success in learning mesh-free solution operators to PDEs [27][28][29], we choose FNOs [26] as a surrogate model for velocity continuation-a process that can be interpreted as a double linearized PDE solve. The main components of FNOs are the Fourier layers, which involve a Fourier transform over the spatial dimensions of their input, followed by a learned pointwise multiplication and an inverse Fourier transform.…”

Section: Fourier Neural Operators For Velocity Continuationmentioning

confidence: 99%

“…To address this challenge, we propose a neural network surrogate for velocity continuation that is capable of mapping seismic images associated with one background model to another with negligible computational cost. Motivated by the success of Fourier neural operators [FNOs,26] in approximating the solution operator of PDEs [27][28][29], we chose them as the architecture for our neural network surrogate. Due to our main interest in accelerating velocity continuation in the context of UQ, we train a survey-specific FNO that acts as a surrogate for velocity continuation for the specific survey at hand.…”

Section: Introductionmentioning

confidence: 99%

Velocity continuation with Fourier neural operators for accelerated uncertainty quantification

Siahkoohi¹,

Louboutin²,

Herrmann³

2022

Preprint

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Seismic imaging is an ill-posed inverse problem that is challenged by noisy data and modeling inaccuracies-due to errors in the background squared-slowness model. Uncertainty quantification is essential for determining how variability in the background models affects seismic imaging. Due to the costs associated with the forward Born modeling operator as well as the high dimensionality of seismic images, quantification of uncertainty is computationally expensive. As such, the main contribution of this work is a survey-specific Fourier neural operator surrogate to velocity continuation that maps seismic images associated with one background model to another virtually for free. While being trained with only 200 background and seismic image pairs, this surrogate is able to accurately predict seismic images associated with new background models, thus accelerating seismic imaging uncertainty quantification. We support our method with a realistic data example in which we quantify seismic imaging uncertainties using a Fourier neural operator surrogate, illustrating how variations in background models affect the position of reflectors in a seismic image.

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Physics-Informed Deep Neural Operator Networks

Goswami,

Bora,

et al. 2023

Computational Methods in Engineering &Amp; The Sciences

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Physics-guided deep learning using Fourier neural operators for solving the acoustic VTI wave equation

Cited by 14 publications

References 0 publications

Physics-Informed Deep Neural Operator Networks

Physics-Informed Deep Neural Operator Networks

Velocity continuation with Fourier neural operators for accelerated uncertainty quantification

Physics-Informed Deep Neural Operator Networks

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