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Deep neural networks (DNNs) for numerical solutions to partial differential equations (PDEs) have exhibited their remarkable merits of meshless methods, dimensionless features, and nonlinear approximation powers. The majority of conventional DNNs are mainly concentrated on the low- or high-dimensional PDE with smooth solutions. In singular problems the DNN does not behave so efficiently as in the smooth problem because of low regularities of the solution. In this paper, we propose a novel adaptive DNN for the PDE with corner singular solutions. In the corner singular problem gradients of solution vary rapidly around some particular vertices or lines. This poses a difficulty in development of DNN solvers. We design adaptive DNN techniques for the corner singularity, which incorporates (a) an adaptive loss function that assigns radial weights to local losses, (b) an adaptive activation function that varies the choice of activation functions from neuron to neuron, and (c) an adaptive sampling strategy that selectively focuses on sampling points near the singular locations. The adaptive DNN with these adaptive schemes greatly enhances approximation accuracy and computation efficiency. This is verified by a comprehensive series of numerical experiments of 2D and 3D corner singular problems. The comparison analyzes with the existing DNN solvers are also made to demonstrate effectiveness of the new method. The L 2 relative errors of the proposed adaptive DNN are reduced by an order of magnitude with respect to several conventional DNN methods. [ABSTRACT FROM AUTHOR]

The path planning and tracking control problem of autonomous vehicle with model matched uncertainty and external disturbance is studied in this paper. A safe lane change zone is designed by considering lane change time, distance, and driving speed. Meanwhile, the candidate paths are generated using cubic quasi-uniform B-spline curve, and the optimal path is selected based on feasibility, comfort, and efficiency criteria. The proposed planning method ensures an efficient and comfortable lane change path without collision with surrounding vehicles. Model uncertainty and external disturbance may affect lane change tracking control of autonomous vehicle. Hence, a fault-tolerant path tracking controller is implemented by using deep neural networks and adjustable zonotope-tube model predictive control. A deep neural network-based controller is proposed to compensate for model matched uncertainty, thereby enhancing the fault tolerance of the control system. Then, an adjustable zonotope-tube model predictive controller is designed to enclose the actual trajectory within a zonotope-tube with the nominal state as the center and the disturbance set as the radius by using the feedback control to achieve the asymptotic stabilization of the closed-loop system. The effectiveness of this path planning and tracking control method is finally verified by numerical simulation. • A lane change path planning method suitable for structured roads is proposed, which is based on the utilization of a safe lane change zone and cubic quasi-uniform B-spline curves. The proposed method ensures an efficient and comfortable lane change path. • A fault-tolerant path tracking controller is presented for autonomous vehicle, which incorporates a deep neural network and adjustable zonotope-tube model predictive control. The controller effectively handles model uncertainty and external disturbances. • The computation of robust positive invariant set is performed using the adjustable zonotope-tube method, which enhances scalability and reduces computational cost. [ABSTRACT FROM AUTHOR]

This paper introduces a novel machine learning approach, called BBATDD (Boosting-Based Algorithm Trained with Drift Detector), that departs from traditional epoch-based methods by adopting a data stream generation strategy from the original dataset. The proposed method is versatile, applicable to a broad range of deep structures and other machine learning architectures. The key to its effectiveness is the conversion of original data into a streaming sequence, which is then fed into the neural network structure. To monitor the learning process and prevent overfitting, a drift detector, commonly used in stream data mining, is employed. Additionally, two methods, ELB and ENT, are introduced to prioritize problematic data elements during the learning process, enhancing overall model performance. Extensive simulations on benchmark datasets (MNIST and CIFAR) validate that BBATDD achieves higher accuracy with significantly fewer batches, without sacrificing generalization capability. For instance, when applied to the MNIST dataset and processing 10 000 batches while comparing loss function values, our approach demonstrates a remarkable 45.6% improvement. [ABSTRACT FROM AUTHOR]

Deep learning-based recommendations have demonstrated impressive performance in improving recommendation accuracy. However, such approaches mainly utilize implicit feedback to predict user preferences and neglect the adverse impact of explicit preference noise, which affects the robustness and reliability of model training. To consider the reliability of both rating input and output, we propose a novel joint deep neural recommendation framework that incorporates rating reliability derived solely from ratings to provide reliable recommendations for active users. Firstly, we introduce a noise detection method based on intuitionistic fuzzy sets to identify incorrect ratings from the perspective of fuzzy preferences and label them to generate a binary rating reliability matrix. Subsequently, we propose a joint deep neural framework that integrates rating reliability to simultaneously capture the high-order features of users and items, yielding predictions with their corresponding reliability probabilities. Finally, to achieve a balance between accuracy and reliability for recommendations, we design a reliability threshold selection strategy based on K-means clustering to find an appropriate threshold. Experimental results on three widely used datasets show that our model achieves an average improvement of 9.4% and 8.0% in the metrics Recall and NDCG, respectively, compared with the closest competitor. This paper provides new insights for integrating rating reliability into a deep neural network to enhance the performance of recommender systems. [ABSTRACT FROM AUTHOR]