Geodesic
Training data set construction based on the Hausdorff metric for numerical dispersion mitigation neural network in seismic modelling
Numerical methods and programming, Tome 24 (2023) no. 2, pp. 195-212.

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The article outlines a strategy for constructing a training data set for a numerical dispersion mitigation network (NDM-net), consisting in the calculation of the full set of seismograms by the finite difference method on a coarse grid and the calculation of the training sample using a fine grid. The training dataset is a small set of seismograms with a certain spatial distribution of wave field sources. After training, the NDM-net allows approximating low-quality coarse-grid seismograms into seismograms with a smaller sampling step. Optimization of the process of constructing a representative training dataset of seismograms is based on minimizing the Hausdorff metric between the training sample and the full set of seismograms. The use of the NDM-net makes it possible to reduce time costs when calculating wave fields on a fine grid.
Keywords: seismograms numerical modelling, numerical dispersion, deep learning, teaching dataset creation. 
@article{VMP_2023_24_2_a5,
     author = {K. A. Gadylshina and D. M. Vishnevskii and K. G. Gadylshin and V. V. Lisitsa},
     title = {Training data set construction based on the {Hausdorff} metric for numerical dispersion mitigation neural network in seismic modelling},
     journal = {Numerical methods and programming},
     pages = {195--212},
     publisher = {mathdoc},
     volume = {24},
     number = {2},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2023_24_2_a5/}
}
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K. A. Gadylshina; D. M. Vishnevskii; K. G. Gadylshin; V. V. Lisitsa. Training data set construction based on the Hausdorff metric for numerical dispersion mitigation neural network in seismic modelling. Numerical methods and programming, Tome 24 (2023) no. 2, pp. 195-212. http://geodesic.mathdoc.fr/item/VMP_2023_24_2_a5/