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We present an original approach to speed up seismic modeling. The approach is based on the combination of the conventional finite difference method and the machine learning technique. The approach is called the 3D Numerical Dispersion Mitigation network, or 3D NDM-net. The method allows quick but inaccurate simulation of the wavefield with further post-processing to suppress the numerical error using the machine learning. According to the numerical experiments, the approach allows speeding up seismic modeling by a factor of up to 15 in the 3D case.