Accelerating Full Waveform Inversion By Transfer Learning

TL;DR

This work addresses the slow and initialization-sensitive nature of NN-based full waveform inversion (FWI) by introducing transfer learning. A pretrained U‑Net maps the adjoint gradient from the first conventional FWI iteration, $\nabla_{\gamma}\mathcal{L}$, to a favorable density scaling function $\hat{\boldsymbol{\gamma}}$ that serves as an initialization for downstream NN-based FWI, yielding faster convergence and cleaner local minima. Across 2D simulations with elliptical and other defects, the transfer learning FWI consistently outperforms conventional FWI, NN-based FWI without pretraining, and conventional FWI with a pretrained initial guess in early iterations and overall reconstruction quality, though not universally in every complex case. The approach reduces dependence on initial NN weights and offers a practical path to more robust, high-quality inversions, while highlighting the need for careful hyperparameter tuning and training-data design. Overall, transfer learning enhances the applicability of NN-based FWI to nondestructive testing scenarios with limited data and computational budgets.

Abstract

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.

Figures (14)

• Figure 1: (a) Set up of the 2D domain. The black dots indicate the position of the sensors in the domain, and the red dots indicate the point of excitation. The blue ellipsoid represents the damage, parameterized using the semi-major and minor axes a,b, the center $(x_c,y_c)$, and the angle $\phi$. (b) Excitation force sine burst with two cycles
• Figure 2: Workflow of the NN-based FWI. The generator network outputs a density scaling function, which is used to solve the equation using a forward solver. A cost function is calculated based on wavefields from the generator network output and the observed wavefields from the true density scaling function, which is then used to calculate the gradient for backpropagation \ref{['eq:chainrule']}.
• Figure 3: Pretraining of the U-Net. The supervised training uses the adjoint gradient from the first iteration of the conventional FWI as the input, and the true density scaling function is the output The U-Net is trained on 800 samples.
• Figure 4: Workflow of the transfer learning NN-based FWI. The pretrained U-Net is used for the FWI. The weights of the pretrained U-Net are updated over iterations such that the misfit between the observed and simulated wavefields are minimized.
• Figure 5: Effect of the weight initialization on the reconstruction of the density scaling function $\gamma$ over iterations.