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.

Due to the abundant neurophysiological information in the electroencephalogram (EEG) signal, EEG signals integrated with deep learning methods have gained substantial traction across numerous real-world tasks. However, the development of supervised learning methods based on EEG signals has been hindered by the high cost and significant label discrepancies to manually label large-scale EEG datasets. Self-supervised frameworks are adopted in vision and language fields to solve this issue, but the lack of EEG-specific theoretical foundations hampers their applicability across various tasks. To solve these challenges, this paper proposes a knowledge-driven cross-view contrastive learning framework (KDC2), which integrates neurological theory to extract effective representations from EEG with limited labels. The KDC2 method creates scalp and neural views of EEG signals, simulating the internal and external representation of brain activity. Sequentially, inter-view and cross-view contrastive learning pipelines in combination with various augmentation methods are applied to capture neural features from different views. By modeling prior neural knowledge based on homologous neural information consistency theory, the proposed method extracts invariant and complementary neural knowledge to generate combined representations. Experimental results on different downstream tasks demonstrate that our method outperforms state-of-the-art methods, highlighting the superior generalization of neural knowledge-supported EEG representations across various brain tasks.