Graph neural networks for full waveform inversion

Abstract In ultrasonic testing, full-waveform inversion (FWI) is employed to recover internal material perturbations by fitting simulated wavefields to 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. While neural network parameterizations and data-driven transfer learning have recently demonstrated superior reconstruction performance, these approaches have been restricted to uniform grids . In this work, we extend this methodology to arbitrarily shaped domains using graph convolutional networks (GCNs). Furthermore, we demonstrate that the inversion of the 3D elastic wave equation can be significantly accelerated by inexpensive pre-training on scalar 2D datasets, resulting in faster convergence and improved reconstruction accuracy. Numerical experiments across diverse experimental setups, with varying emitter and receiver distributions, and material properties, confirm that the proposed method provides a robust, computationally efficient solution for ultrasonic evaluation on irregular geometric domains.