Three-Dimensional High-Fidelity Surrogate Modeling of Frequency-Domain Airborne Electromagnetics Based on Hybrid DeepONet-Fourier Neural Operator

To improve the efficiency of 3D forward modeling in airborne electromagnetic (AEM) methods, we propose a novel high-fidelity surrogate modeling approach based on the Hybrid DeepONet-Fourier Neural Operator (HDF). This method leverages the DeepONet’s Branch-Trunk network to the input data, which is then processed in a higher-dimensional Fourier space for enhanced information extraction and learning. The architecture preserves the deep neural network’s capacity to solve multiple partial differential equations (PDEs) while utilizing Fourier transforms to improve generalization. The training dataset was generated using the Gaussian random field (GRF) method, which efficiently creates smooth, random geometric shapes across various scales, representing complex geological structures. The theoretical experiments demonstrate that the hybrid architecture outperforms conventional DeepONet and FNO models under the same training conditions, it reduces the relative errors by nearly an order of magnitude. When applied to the real geological model of the Byneset region in Norway, the hybrid architecture achieves a prediction accuracy comparable to traditional numerical methods, and outperforms DeepONet and FNO in terms of prediction errors. Additionally, the proposed approach is approximately 1000 times faster than the finite difference methods, making it a highly efficient solver for future data inversions.