EFKAN: A KAN-Integrated Neural Operator For Efficient Magnetotelluric Forward Modeling

2025-02-04

AI Summary

To address the poor interpretability, susceptibility to overfitting, and weak generalization of conventional MLP-based neural operators in magnetotelluric (MT) forward modeling, this paper proposes EFKAN—a novel neural operator integrating the Kolmogorov–Arnold Network (KAN) with the Fourier Neural Operator (FNO). EFKAN replaces the standard MLP backbone with KAN: an FNO branch captures frequency-domain features of resistivity models, while a KAN trunk enables high-fidelity mapping from resistivity/phase inputs to arbitrary spatial–frequency output points. This architecture jointly enhances interpretability, generalization capability, and spatio-spectral modeling fidelity. Experimental results demonstrate that EFKAN achieves significantly higher accuracy than MLP-based methods in predicting apparent resistivity and phase, while accelerating computation by over two orders of magnitude compared to traditional numerical solvers.

Technology Category

• Machine Learning: Mixture of Experts (MoE)
• Search and Optimization: Metareasoning and Metaheuristics
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Web Mining and Content Analysis: Large pretrained models with web data
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

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.

Problem

• Improve magnetotelluric forward modeling accuracy
• Enhance neural operator efficiency with KAN
• Overcome MLP limitations in neural operators

Innovation

• Integrates Fourier and Kolmogorov-Arnold networks
• Enhances accuracy in electromagnetic field modeling
• Improves computational speed over traditional methods