A general approach to seismic inversion with automatic differentiation

Zhu, Weiqiang; Xu, Kailai; Darve, Eric; Beroza, Gregory C.

doi:10.1016/j.cageo.2021.104751

Cited by 44 publications

(28 citation statements)

References 50 publications

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“…Hughes et al (2019), J. Zhu et al (2021) showed that the reverse-mode of AD is mathematically equivalent to the adjoint-state method in solving the wave-equation inversion problem; thus, the reverse-mode of AD can be used to automatically compute the velocity gradient with respect to the LS feature misfit using the chain rule.…”

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confidence: 99%

Seismic Inversion by Hybrid Machine Learning

Chen

Saygin

2021

JGR Solid Earth

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We present a hybrid machine learning (HML) inversion method, which uses the latent space (LS) features of a convolutional autoencoder (CAE) to estimate the subsurface velocity model. The LS features are the effective low‐dimensional representation of the high‐dimensional seismic data. However, no equations exist to describe the relationship between the perturbation of an LS feature and the velocity perturbation. To address this problem, we use automatic differentiation (AD) to connect the two terms. Following this step, we use the wave‐equation inversion to invert the LS features for the subsurface velocity model. The HML misfit function measures the LS feature differences between the observed and predicted seismic data in a low‐dimensional space, which is less affected by the cycle‐skipping problem compared to the waveform mismatch in a high‐dimensional space. A low dimensional LS feature mainly contains the kinematic information of seismic data, while a large dimensional LS feature can also preserve the dynamic information of seismic data. Therefore, the HML inversion can recover the subsurface velocity model in a multiscale approach by inverting the LS features with different dimensions. Based on the different ways of utilizing AD to compute the velocity gradient, we propose full‐ and semi‐automatic approaches to solve this problem. These two approaches are mathematically equivalent; the former is easier to implement, while the latter is computationally more efficient. Numerical tests show that the HML inversion method can effectively recover both the low‐ and high‐wavenumber velocity information by inverting the LS features with different dimensions.

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confidence: 99%

Seismic Inversion by Hybrid Machine Learning

Chen

Saygin

2021

JGR Solid Earth

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“…In order to compute PDE loss, output fields are automatically differentiated with respect to input coordinates. PINNs are now applied to various disciplines including material science (Lu et al, 2020;Shukla et al, 2020), geology (Li et al, 2020a;Zhu et al, 2021), andbiophysics (Fathi et al, 2020). Although its wide range of applicability is very promising, it shows Figure 1: Overall PIXEL architecture for a PDE solver slower convergence rates and is vulnerable to the highly nonlinear PDEs (Krishnapriyan et al, 2021;Wang et al, 2022a).…”

Section: Related Workmentioning

confidence: 99%

PIXEL: Physics-Informed Cell Representations for Fast and Accurate PDE Solvers

Kang¹,

Byeonghyeon²,

Hong³

et al. 2022

Preprint

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With the increases in computational power and advances in machine learning, data-driven learning-based methods have gained significant attention in solving PDEs. Physics-informed neural networks (PINNs) have recently emerged and succeeded in various forward and inverse PDEs problems thanks to their excellent properties, such as flexibility, mesh-free solutions, and unsupervised training. However, their slower convergence speed and relatively inaccurate solutions often limit their broader applicability in many science and engineering domains. This paper proposes a new kind of data-driven PDEs solver, physics-informed cell representations (PIXEL), elegantly combining classical numerical methods and learning-based approaches. We adopt a grid structure from the numerical methods to improve accuracy and convergence speed and overcome the spectral bias presented in PINNs. Moreover, the proposed method enjoys the same benefits in PINNs, e.g., using the same optimization frameworks to solve both forward and inverse PDE problems and readily enforcing PDE constraints with modern automatic differentiation techniques. We provide experimental results on various challenging PDEs that the original PINNs have struggled with and show that PIXEL achieves fast convergence speed and high accuracy.

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“…In recent years, neural network methods are becoming an attractive alternative for solving partial differential equations (PDEs) arising from applications such as fluid dynamics [2][3][4], quantum mechanics [5][6][7], molecular dynamics [8], material sciences [9] and geophysics [10,11]. In contrast to most traditional numerical approaches, methods based on neural networks are naturally meshfree and intrinsically nonlinear therefore can be applied without going through the cumbersome step of mesh generation and could be more potentially applicable to complicated nonlinear problems.…”

Section: Introductionmentioning

confidence: 99%

PFNN-2: A Domain Decomposed Penalty-Free Neural Network Method for Solving Partial Differential Equations

Sheng¹,

Liu²

2022

Preprint

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A new penalty-free neural network method, PFNN-2, is presented for solving partial differential equations, which is a subsequent improvement of our previously proposed PFNN method [1]. PFNN-2 inherits all advantages of PFNN in handling the smoothness constraints and essential boundary conditions of self-adjoint problems with complex geometries, and extends the application to a broader range of non-self-adjoint time-dependent differential equations. In addition, PFNN-2 introduces an overlapping domain decomposition strategy to substantially improve the training efficiency without sacrificing accuracy. Experiments results on a series of partial differential equations are reported, which demonstrate that PFNN-2 can outperform state-of-the-art neural network methods in various aspects such as numerical accuracy, convergence speed, and parallel scalability.

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A general approach to seismic inversion with automatic differentiation

Cited by 44 publications

References 50 publications

Seismic Inversion by Hybrid Machine Learning

Seismic Inversion by Hybrid Machine Learning

PIXEL: Physics-Informed Cell Representations for Fast and Accurate PDE Solvers

PFNN-2: A Domain Decomposed Penalty-Free Neural Network Method for Solving Partial Differential Equations

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