Abstract Diffusion models have achieved remarkable success in image super‐resolution by addressing issues such as transition smoothing, insufficient high‐frequency information, and training instability encountered in regression‐based and GAN‐based models. However, challenges persist when applying diffusion models to image super‐resolution, including randomness, inadequate conditional information, high computational costs, and network architecture complexities. In this article, the authors introduce a diffusion model based on Mean‐Reverting Stochastic Differential Equations (SDE), and propose the use of ENAFBlocks instead of traditional ResBlocks to enhance model performance in noise prediction. The Mean‐Reverting SDE effectively mitigates the randomness of the diffusion model by leveraging low‐resolution images as means. Additionally, an LR Encoder is introduced to capture hidden information from LR images, providing a more robust condition for stable result generation by the noise predictor. To efficiently handle high‐resolution images within limited GPU memory, the method employs adaptive aggregate sampling, which merges overlapping regions smoothly using weighted averaging. Furthermore, color variations are addressed during diffusion model sampling through color correction. Extensive experiments on CelebA, DIV2K, and Urban100 demonstrate that the method outperforms state‐of‐the‐art diffusion models like IDM, with a PSNR improvement of 0.22 dB, FID reduction of 2.35, and LPIPS reduction of 0.05 on the DIV2K dataset, along with a reduced parameter count and faster inference time.

As a new type of seismic source, the high-speed train (HST) seismic source has great application potential in subsurface imaging in terms of high intensity, strong repeatability and wide distribution compared with traditional seismic sources. However, the HST seismic data are severely interfered in the time-space domain due to the complex mobile combination source. Besides, the body waves are almost swamped by strong surface waves. Therefore, it is difficult to directly use this kind of seismic data for subsurface exploration. Considering the characteristic differences between the surface and body waves in the frequency-wavenumber (F-K) domain, it is more conducive to separate the surface and body waves for the HST seismic data in the F-K domain, so as to use different wavefield information in sequence. Therefore, in this study, we attempt to apply the inversion method with F-K spectrum as the objective function to HST seismic data, which aims to more effectively utilize the surface and body waves therein. In addition, to alleviate the coupling effect between P-wave and S-wave in elastic waveform inversion, we introduce the divided-offset strategy to further improve the quality of the inverted P-wave and S-wave velocities. Numerical experiments indicate that the proposed inversion method is beneficial to make better use of the surface and body waves in HST seismic data, and is expected to provide more insights on the use of HST seismic data for subsurface monitoring and detection.

The high-speed train (HST), as a special kind of seismic source, can be simplified as a mobile combination source. The HST-induced seismic data (also known as HST seismic data) contains rich geological structural information. However, HST seismic data interfere highly in space and time and their spectra have narrow-band separation spectral characteristics in frequency domain. It is very difficult to effectively extract the geological structural information contained in HST seismic data. In this work, we try to use the elastic wave equation traveltime inversion (EWTI) method to explore the subsurface velocity information using the seismic data induced by HSTs running on viaducts, which is conducive to providing a more reliable initial model to serve full waveform inversion (FWI). However, as mentioned previously, HST seismic data are highly complex, which makes the EWTI method based on first-break picking no longer applicable to them. Therefore, we apply dynamic time warping (DTW) to obtain the time shifts between observed HST-induced seismic data and synthetic HST-induced seismic data. Based on the time shifts obtained by DTW, the subsurface velocity model can be updated by establishing the misfit function and calculating the gradient. Numerical experiments using the simple velocity anomaly model and the Marmousi2 model show that the DTW-based EWTI method is able to obtain the large-scale background model and provide a reliable initial model to serve FWI. The results in this work also demonstrate the considerable potential of underground exploration using HST-induced seismic data.

The factorization machine models attract significant attention nowadays since they improve recommendation performance by incorporating context information into recommendation modeling. However, traditional factorization machine models often adopt the point-wise learning method for model parameter learning, as well as only model the linear interactions between features. They substantially fail to capture the complex interactions among features, which degrades the performance of factorization machine models. In this research, we propose a neural pairwise ranking factorization machine for item recommendation, namely NPRFM, which integrates the multi-layer perceptual neural networks into the pairwise ranking factorization machine model. Specifically, to capture the high-order and nonlinear interactions among features, we stack a multi-layer perceptual neural network over the bi-interaction layer, which encodes the second-order interactions between features. Moreover, instead of the prediction of the absolute scores, the pair-wise ranking model is adopted to learn the relative preferences of users. Since NPRFM does not take into account the importance of feature interactions, we propose a new variant of NPRFM, which learns the importance of feature interactions by introducing the attention mechanism . The empirical results on real-world datasets indicate that the proposed neural pairwise ranking factorization machine outperforms the traditional factorization machine models.