Seeking effective numerical approximations for partial differential equations (PDEs) is a major challenge in modern science and technology. Recently, AI-inspired data-driven solvers, such as neural operators, have achieved great success in quickly PDE solving. However, in the design of neural operators, the processing of frequency domain information is crucial, while the importance of low-frequency information is excessively overlooked. In order to reduce low-frequency error in PDE solving, we propose the multi scale spectral mixture neural operator (MSSMNO) architecture and design a residual learning structure that transfers residuals in multi-scale cycle by combining the frequency domain learning patterns of the FNO method. Meanwhile, we designed interpolation operator and restriction operator to effectively transmit and reconstruct high-frequency information in MSSMNO. Experimentally, MSSMNO achieves state-of-the-art and yields a relative error reduction of 21.9% averaged on four classical benchmarks.

Depression is a prevalent global mental health issue that significantly impacts both individuals and societies. Current methods often overlook the heterogeneity of depressive symptoms and fail to fully leverage available data, underscoring the need for more advanced computational methods DTI prediction. This paper introduces KGM4DTI, a multi-semantic, multi-view, and multi-level meta-path Transformer framework that integrates Transformer and GNN. KGM4DTI effectively captures both global semantic and local structural information between interaction pairs within a depression knowledge graph (DepKG), which comprises 2,258 drugs, 3,360 proteins, 6 subtypes of depression, 196 phenotypes, and 238 pathways. Comparative experiments have demonstrated that KGM4DTI significantly outperforms existing state-of-the-art methods, achieving an AUROC of 99.72 and an AUPR of 99.76. The robustness of framework is further confirmed through extensive ablation studies, which highlight the crucial role of integrating both global and local information. These results underscore the potential of KGM4DTI in accurately predicting DTI. This approach has promising implications for drug discovery, particularly in developing effective treatments for depression, and could extend its applicability to broader mental health disorders. The data and code are available at https://github.com/Tianxyuu/KGM4DTI/.

MOTIVATION: Protein-protein interaction sites (PPIS) are crucial for deciphering protein action mechanisms and related medical research, which is the key issue in protein action research. Recent studies have shown that graph neural networks have achieved outstanding performance in predicting PPIS. However, these studies often neglect the modeling of information at different scales in the graph and the symmetry of protein molecules within three-dimensional space. RESULTS: In response to this gap, this article proposes the MEG-PPIS approach, a PPIS prediction method based on multi-scale graph information and E(n) equivariant graph neural network (EGNN). There are two channels in MEG-PPIS: the original graph and the subgraph obtained by graph pooling. The model can iteratively update the features of the original graph and subgraph through the weight-sharing EGNN. Subsequently, the max-pooling operation aggregates the updated features of the original graph and subgraph. Ultimately, the model feeds node features into the prediction layer to obtain prediction results. Comparative assessments against other methods on benchmark datasets reveal that MEG-PPIS achieves optimal performance across all evaluation metrics and gets the fastest runtime. Furthermore, specific case studies demonstrate that our method can predict more true positive and true negative sites than the current best method, proving that our model achieves better performance in the PPIS prediction task. AVAILABILITY AND IMPLEMENTATION: The data and code are available at https://github.com/dhz234/MEG-PPIS.git.