Stabilized Crank-Nicolson/Adams-Bashforth Schemes for Phase Field Models - Volume 3 Issue 1 - Xinlong Feng, Tao Tang, Jiang Yang

When PINNs solve the Navier–Stokes equations, the loss function has a gradient imbalance problem during training. It is one of the reasons why the efficiency of PINNs is limited. This paper proposes a novel method of adaptively adjusting the weights of loss terms, which can balance the gradients of each loss term during training. The weight is updated by the idea of the minmax algorithm. The neural network identifies which types of training data are harder to train and forces it to focus on those data before training the next step. Specifically, it adjusts the weight of the data that are difficult to train to maximize the objective function. On this basis, one can adjust the network parameters to minimize the objective function and do this alternately until the objective function converges. We demonstrate that the dynamic weights are monotonically non-decreasing and convergent during training. This method can not only accelerate the convergence of the loss, but also reduce the generalization error, and the computational efficiency outperformed other state-of-the-art PINNs algorithms. The validity of the method is verified by solving the forward and inverse problems of the Navier–Stokes equation.

Multi-object pedestrian tracking plays a crucial role in autonomous driving systems, enabling accurate perception of the surrounding environment. In this paper, we propose a comprehensive approach for pedestrian tracking, combining the improved YOLOv8 object detection algorithm with the OC-SORT tracking algorithm. First, we train the improved YOLOv8 model on the Crowdhuman dataset for accurate pedestrian detection. The integration of advanced techniques such as softNMS, GhostConv, and C3Ghost Modules results in a remarkable precision increase of 3.38% and an mAP@0.5:0.95 increase of 3.07%. Furthermore, we achieve a significant reduction of 39.98% in parameters, leading to a 37.1% reduction in model size. These improvements contribute to more efficient and lightweight pedestrian detection. Next, we apply our enhanced YOLOv8 model for pedestrian tracking on the MOT17 and MOT20 datasets. On the MOT17 dataset, we achieve outstanding results with the highest HOTA score reaching 49.92% and the highest MOTA score reaching 56.55%. Similarly, on the MOT20 dataset, our approach demonstrates exceptional performance, achieving a peak HOTA score of 48.326% and a peak MOTA score of 61.077%. These results validate the effectiveness of our approach in challenging real-world tracking scenarios.