Graph Neural Networks for Full Waveform Inversion

In ultrasonic testing, full waveform inversion (FWI) is employed to recover internal material perturbations by fitting the simulated wave fields with sparsely measured wave signals at sensor locations using gradient-based optimization. Since the underlying optimization problem is inherently ill-posed, the resulting material fields without regularization contain substantial artifacts. Neural network parameterizations have been shown to produce superior reconstructions. Incorporating prior knowledge through data-driven transfer learning can further accelerate the reconstruction. To date, such approaches have been limited to uniform grids treated using convolutional neural networks. In this work, we extend this methodology to arbitrarily shaped domains using graph convolutional networks (GCN). The GCN-based FWI exhibits strong generalization capabilities. The proposed approach for the 3D elastic wave equation can be accelerated through inexpensive pre-training on a scalar 2D dataset, resulting in faster training and more accurate reconstructions. Numerical experiments demonstrate that the proposed method can generalize well to complex 2D and 3D geometries with diverse experimental setups involving different sensor positions, sources, and material properties.