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Wasserstein loss function

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Journal Article
Journal: The Leading Edge
Published: 01 March 2017
The Leading Edge (2017) 36 (3): 208–214.
.... In this paper, we start by explaining the basics of the problem followed by discussions of DNNs and the Wasserstein loss function. Next, we introduce the general workflow used to train our DNN. After that, we discuss our performance results and some of our findings regarding network architectural parameters...
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Journal Article
Journal: Geophysics
Published: 22 September 2022
Geophysics (2022) 87 (6): R401–R411.
.... Cycle-GAN ( Wang et al., 2019b ) and Wasserstein Cycle-GAN (Wcycle-GAN) ( Cai et al., 2020 ) have the same neural network architecture. The former uses cross-entropy as the loss function and the latter uses Wasserstein distance as the loss function to achieve acoustic impedance inversion, respectively...
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Journal Article
Journal: Geophysics
Published: 21 October 2024
Geophysics (2024) 89 (6): F117–F128.
... to waveform inversion, and Villani (2003) proposes a convex mismatch function based on the Wasserstein-2 ( W 2 ) metric. The OT distance has some prerequisites such as equal mass and normalization. Thus, when comparing seismic data using the W 2 metric, data preprocessing must...
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Journal Article
Journal: Geophysics
Published: 05 January 2018
Geophysics (2018) 83 (1): R43–R62.
.... The quadratic Wasserstein metric has proven to have many ideal properties with regard to convexity and insensitivity to noise. When the observed and predicted seismic data are considered to be two density functions, the quadratic Wasserstein metric corresponds to the optimal cost of rearranging one density...
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Journal Article
Journal: Geophysics
Published: 15 June 2023
Geophysics (2023) 88 (4): R469–R483.
...Hao Zhang; Weiguang He; Jianwei Ma ABSTRACT The conventional least-squares misfit function compares synthetic data to observed data in a point-by-point style. The Wasserstein distance function, also called the optimal transport function, matches patterns. The kinematic information of seismograms...
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Journal Article
Journal: Geophysics
Published: 05 September 2018
Geophysics (2018) 83 (5): R515–R540.
... on the accuracy of the initial model, they can still suffer from cycle skipping, and also from a loss of resolution. The design of adequate penalization functions might also be problematic, due to the high sensitivity of the resulting misfit function to this design ( Pladys et al., 2017 ). In this study, we...
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Journal Article
Journal: The Leading Edge
Published: 01 November 2019
The Leading Edge (2019) 38 (11): 872a1–872a9.
... community. For example, similar loss functions, such as Wasserstein ( Yang et al., 2018 ; Sun and Alkhalifah, 2019 ), were first used in the DL community in Frogner et al. (2015) . They gained wide attention and were integrated in GAN architectures ( Gulrajani et al., 2017 ). The connection between...
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Journal Article
Published: 22 April 2022
Bulletin of the Seismological Society of America (2022) 112 (4): 1979–1996.
... networks (GANs) to develop a new framework for synthesizing earthquake acceleration time histories. Our approach extends the Wasserstein GAN formulation to allow for the generation of ground motions conditioned on a set of continuous physical variables. Our model is trained to approximate the intrinsic...
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Journal Article
Journal: The Leading Edge
Published: 01 December 2019
The Leading Edge (2019) 38 (12): 923–933.
... learned by the generator and the actual data distribution. The WGANs gradient penalty (WGANs-GP) loss function ( Gulrajani et al., 2017 ) uses gradient penalty to additionally clip the weights of the discriminator. It succesfully addresses common problems observed in general GANs, such as unstable...
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Journal Article
Published: 10 September 2024
Bulletin of the Seismological Society of America (2024) 114 (6): 2846–2868.
... the deterministic LF waveforms with stochastic HF waveforms to produce BB ground motions ( Kamae et al. , 1998 ; Hartzell et al. , 1999 ; Liu et al. , 2006 ; Graves and Pitarka, 2010 ; Mai et al. , 2010 ). Mai et al. (2010) presented an approach in which HF is computed by convolving source time function...
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Journal Article
Journal: Geophysics
Published: 28 October 2019
Geophysics (2019) 84 (6): R923–R945.
... for designing misfit functions by measuring the distance between the matching filter and a representation of the Dirac delta function using optimal transport theory. We have used the Wasserstein W 2 distance, which provides us with the optimal transport between two probability distribution functions. Unlike...
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Journal Article
Journal: Geophysics
Published: 20 February 2023
Geophysics (2023) 88 (2): M87–M103.
... layer for the classification task and does fit the Wasserstein distance, which is a regression task; the sigmoid function is removed in the last layer, as is the log operator of the loss functions of G and D . The gradient penalty technique ( Gulrajani et al., 2017 ) is used to ensure stable...
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Journal Article
Journal: Geophysics
Published: 05 January 2018
Geophysics (2018) 83 (1): 1JF–4JF.
... ABSTRACT In this article, the Editor of G eophysics provides an overview of all technical articles in this issue of the journal. Trace-by-trace comparison with the quadratic Wasserstein metric works remarkably well with the adjoint-state method as a misfit function in full-waveform inversion...
Journal Article
Published: 01 February 2024
Earthquake Spectra (2024) 40 (1): 647–673.
... are a precursor for subsequent loss analyses, repair and recovery modeling, and interdependent systems analyses. The common practice is to use fragility functions to predict systems’ performance while recognizing the influence of inherent sources of uncertainty. A fragility function is often defined...
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Journal Article
Published: 08 December 2022
Bulletin of the Seismological Society of America (2023) 113 (1): 453–467.
...‐Wasserstein loss with gradient penalty (GP) using an Adam optimization method with parameters of β 1 = 0 and β 2 = 0.9 , and the learning rate of 0.0001 for generator and 0.0005 for discriminator networks. We fed the CGAN network using a batch size of 32. Discriminator and generator...
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Journal Article
Journal: Geophysics
Published: 03 February 2025
Geophysics (2025) IM47–IM58.
... ). This loss function is based on the assumption that for a highly accurate transformation between two domains, the original image x should be identical to the image obtained after applying forward and reverse transformations, i.e.,  G B A ( G A B ( x ) ) and vice versa. To guide...
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Journal Article
Journal: Geophysics
Published: 22 March 2024
Geophysics (2024) 89 (3): R231–R246.
..., multiparameter (e.g. velocity and Q ) waveform inversion can be used to mitigate these problems. Benefiting from the theory of Q -compensated wavefield propagation, we develop a Q -compensated joint multiparameter waveform inversion method to weaken the nonlinearity of the FWI objective function, which enables...
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Journal Article
Published: 01 February 2019
Earthquake Spectra (2019) 35 (1): 193–210.
... (see online Appendix C for more information). The SP3 software tool is used to run FEMA P-58 analyses in both cases. As part of the development of the HAZUS methodology ( Whitman et al. 1997 , Kircher et al. 1997a , 1997b ), loss functions were calibrated by comparing predicted loss with observed...
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Journal Article
Published: 20 September 2024
Bulletin of the Seismological Society of America (2024) 114 (6): 2912–2925.
... is to learn a conditional log‐normal distribution over the expected GMPE output: both the input and the output of the ConvCNP are expressed in terms of log( g ). The loss function used to train the model is a linear combination of Fréchet inception distance (FID; Dowson and Landau, 1982 ; Heusel et al...
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Journal Article
Journal: Geophysics
Published: 04 December 2024
Geophysics (2025) 90 (1): KS15–KS30.
... waveform inversion method based on the envelope objective function, which has been successfully applied to crosshole GPR data ( Liu et al., 2022 ). In addition, inspired by similarities between seismic and GPR surveys, methods based on optimal transmission distance and convolutional Wasserstein distance...
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