  Full waveform inversion (FWI) is a powerful tool for reconstructing material
fields based on sparsely measured data obtained by wave propagation. For
specific problems, discretizing the material field with a neural network (NN)
improves the robustness and reconstruction quality of the corresponding
optimization problem. We call this method NN-based FWI. Starting from an
initial guess, the weights of the NN are iteratively updated to fit the
simulated wave signals to the sparsely measured data set. For gradient-based
optimization, a suitable choice of the initial guess, i.e., a suitable NN
weight initialization, is crucial for fast and robust convergence.
  In this paper, we introduce a novel transfer learning approach to further
improve NN-based FWI. This approach leverages supervised pretraining to provide
a better NN weight initialization, leading to faster convergence of the
subsequent optimization problem. Moreover, the inversions yield physically more
meaningful local minima. The network is pretrained to predict the unknown
material field using the gradient information from the first iteration of
conventional FWI. In our computational experiments on two-dimensional domains,
the training data set consists of reference simulations with arbitrarily
positioned elliptical voids of different shapes and orientations. We compare
the performance of the proposed transfer learning NN-based FWI with three other
methods: conventional FWI, NN-based FWI without pretraining and conventional
FWI with an initial guess predicted from the pretrained NN. Our results show
that transfer learning NN-based FWI outperforms the other methods in terms of
convergence speed and reconstruction quality.
