Autonomous underwater vehicles (AUVs) have been widely used in ocean missions. When they fail in the ocean, it is important to predict their trajectory. Existing methods rely heavily on historical trajectory data while overlooking the influence of the ocean environment on an AUV’s trajectory. At the same time, these methods fail to use the dependency between variables in the trajectory. To address these challenges, this paper proposes an AUV trajectory prediction model known as the nonlinear Kepler optimization algorithm–bidirectional long short-term memory–time-variable attention (NKOA-BiLSTM-TVA) model. This paper introduces opposition-based learning during the initialization process of the KOA and improves the algorithm by incorporating a nonlinear factor into the planet position update process. We designed an attention mechanism layer that spans both time and variable dimensions, called TVA. TVA can extract features from both the time and variable dimensions of the trajectory and use the dependency between trajectory variables to predict the trajectory. First, the model uses a convolutional neural network (CNN) to extract spatial features from the trajectory. Next, it combines a BiLSTM network with TVA to predict the AUV’s trajectory. Finally, the improved NKOA is used to optimize the model’s hyperparameters. Experimental results show that the NKOA-BiLSTM-TVA model has an excellent parameter optimization effect and higher prediction accuracy in AUV trajectory prediction tasks. It also achieves excellent results in ship trajectory prediction.

The accurate prediction of drift trajectories holds paramount significance for disaster response and navigational safety. The future positions of underwater drifters in the ocean are closely related to their historical drift patterns. Additionally, leveraging the complex dependencies between drift trajectories and ocean currents can enhance the accuracy of predictions. Building upon this foundation, we propose a Transformer model based on double-branch adaptive span attention (DBASformer), aimed at capturing the multivariate time-series relationships within drift history data and predicting drift trajectories in future periods. DBASformer can predict drift trajectories more accurately. The proposed adaptive span attention mechanism exhibits enhanced flexibility in the computation of attention weights, and the double-branch attention structure can capture the cross-time and cross-dimension dependencies in the sequences. Finally, our method was evaluated using datasets containing buoy data with ocean current velocities and Autonomous Underwater Vehicle (AUV) data. The raw data underwent cleaning and alignment processes. Comparative results with five alternative methods demonstrate that DBASformer improves prediction accuracy.

The rapid development of high-throughput technology has generated a large amount of protein–protein interaction (PPI) data, which provide a large amount of data support for constructing dynamic protein–protein interaction networks (PPINs). Constructing dynamic PPINs and applying them to recognize protein complexes has become a hot research topic. Most existing methods for complex recognition cannot fully mine the information of PPINs. To address this problem, we propose a construction method of dynamic weighted protein network by multi-level embedding (DWPNMLE). It can reflect the protein network’s dynamics and the protein network’s higher-order proximity. Firstly, the protein active period is calculated to divide the protein subnetworks at different time points. Then, the connection probability is used for the proteins possessing the same time points to judge whether there is an interaction relationship between them. Then, the corresponding protein subnetworks (multiple adjacency matrices) are constructed. Secondly, the multiple feature matrices are constructed using one-hot coding with the gene ontology (GO) information. Next, the first embedding is performed using variational graph auto-encoders (VGAEs) to aggregate features efficiently, followed by the second embedding using deep attributed network embedding (DANE) to strengthen the node representations learned in the first embedding and to maintain the first-order and higher-order proximity of the original network; finally, we compute the cosine similarity to obtain the final dynamic weighted PPIN. To evaluate the effectiveness of DWPNMLE, we apply four classical protein-complex-recognition algorithms on the DWPNMLE and compare them with two other dynamic protein network construction methods. The experimental results demonstrate that DWPNMLE significantly enhances the accuracy of complex recognition with high robustness, and the algorithms’ efficiency is also within a reasonable range.