EFKAN: A KAN-Integrated Neural Operator For Efficient Magnetotelluric Forward Modeling
This work addresses accuracy and efficiency issues in magnetotelluric forward modeling for geophysical applications, representing an incremental improvement by integrating KANs into neural operators.
The paper tackles the problem of improving accuracy in magnetotelluric forward modeling by proposing EFKAN, a neural operator that integrates Kolmogorov-Arnold networks with Fourier neural operators, achieving higher accuracy in obtaining apparent resistivity and phase compared to existing neural operators with MLPs and outperforming traditional numerical methods in computational speed.
Magnetotelluric (MT) forward modeling is fundamental for improving the accuracy and efficiency of MT inversion. Neural operators (NOs) have been effectively used for rapid MT forward modeling, demonstrating their promising performance in solving the MT forward modeling-related partial differential equations (PDEs). Particularly, they can obtain the electromagnetic field at arbitrary locations and frequencies. In these NOs, the projection layers have been dominated by multi-layer perceptrons (MLPs), which may potentially reduce the accuracy of solution due to they usually suffer from the disadvantages of MLPs, such as lack of interpretability, overfitting, and so on. Therefore, to improve the accuracy of MT forward modeling with NOs and explore the potential alternatives to MLPs, we propose a novel neural operator by extending the Fourier neural operator (FNO) with Kolmogorov-Arnold network (EFKAN). Within the EFKAN framework, the FNO serves as the branch network to calculate the apparent resistivity and phase from the resistivity model in the frequency domain. Meanwhile, the KAN acts as the trunk network to project the resistivity and phase, determined by the FNO, to the desired locations and frequencies. Experimental results demonstrate that the proposed method not only achieves higher accuracy in obtaining apparent resistivity and phase compared to the NO equipped with MLPs at the desired frequencies and locations but also outperforms traditional numerical methods in terms of computational speed.