  Accurate forward modeling is important for solving inverse problems. An
inaccurate wave-equation simulation, as a forward operator, will offset the
results obtained via inversion. In this work, we consider the case where we
deal with incomplete physics. One proxy of incomplete physics is an inaccurate
discretization of Laplacian in simulation of wave equation via
finite-difference method. We exploit intrinsic one-to-one similarities between
timestepping algorithm with Convolutional Neural Networks (CNNs), and propose
to intersperse CNNs between low-fidelity timesteps. Augmenting neural networks
with low-fidelity timestepping algorithms may allow us to take large timesteps
while limiting the numerical dispersion artifacts. While simulating the
wave-equation with low-fidelity timestepping algorithm, by correcting the
wavefield several time during propagation, we hope to limit the numerical
dispersion artifact introduced by a poor discretization of the Laplacian. As a
proof of concept, we demonstrate this principle by correcting for numerical
dispersion by keeping the velocity model fixed, and varying the source
locations to generate training and testing pairs for our supervised learning
algorithm.
