EFKAN: A KAN-integrated neural operator for efficient magnetotelluric forward modeling

Forward modeling is the cornerstone of magnetotelluric (MT) inversion. Neural operators have been successfully applied to solve partial differential equations, demonstrating encouraging performance in rapid MT forward modeling. In particular, they can obtain the electromagnetic field at arbitrary locations and frequencies, which is meaningful for MT forward modeling. In conventional neural operators, the projection layers have been dominated by classical multi-layer perceptrons, which may reduce the precision of solution because they usually suffer from the disadvantages of multi-layer perceptrons, such as lack of interpretability, overfitting, etc. Therefore, to improve the accuracy of the MT forward modeling with neural operators, we integrate the Fourier neural operator with the Kolmogorov–Arnold network (KAN). Specifically, we adopt KAN as the trunk network instead of the classic multi-layer perceptrons to project the resistivity and phase, determined by the branch network-Fourier neural operator, to the desired locations and frequencies. Experimental results demonstrate that the proposed method can achieve high precision in obtaining apparent resistivity and phase at arbitrary frequencies and/or locations with rapid computational speed.