Tie Zhang

Tie Zhang, Yanli Chen

We present a weak finite element method for elliptic problems in one space dimension. Our analysis shows that this method has more advantages than the known weak Galerkin method proposed for multi-dimensional problems, for example, it has higher accuracy and the derived discrete equations can be solved locally, element by element. We derive the optimal error estimates in the discrete $H^1$-norm, the $L_2$-norm and $L_\infty$-norm, respectively. Moreover, some superconvergence results are also given. Finally, numerical examples are provided to illustrate our theoretical analysis.

Yanli Chen, Tie Zhang

We propose a weak Galerkin(WG) finite element method for solving the one-dimensional Burgers' equation. Based on a new weak variational form, both semi-discrete and fully-discrete WG finite element schemes are established and analyzed. We prove the existence of the discrete solution and derive the optimal order error estimates in the discrete $H^1$-norm and $L^2$-norm, respectively. Numerical experiments are presented to illustrate our theoretical analysis.

Tie Zhang, Tao Lin

We study the weak Galerkin finite element method for Stokes problem. A new weak Galerkin finite element velocity-pressure space pair is presented which satisfies the discrete inf-sup condition. Based on this space pair, we establish a stable weak Galerkin approximation scheme without adding any stability term or penalty term. Then, we further derive the optimal error estimates for velocity and pressure approximations, respectively. Numerical experiments are provided to illustrate the theoretical analysis.

Yifei Cheng, Li Shen, Linli Xu et al.

Gradient compression with error compensation has attracted significant attention with the target of reducing the heavy communication overhead in distributed learning. However, existing compression methods either perform only unidirectional compression in one iteration with higher communication cost, or bidirectional compression with slower convergence rate. In this work, we propose the Local Immediate Error Compensated SGD (LIEC-SGD) optimization algorithm to break the above bottlenecks based on bidirectional compression and carefully designed compensation approaches. Specifically, the bidirectional compression technique is to reduce the communication cost, and the compensation technique compensates the local compression error to the model update immediately while only maintaining the global error variable on the server throughout the iterations to boost its efficacy. Theoretically, we prove that LIEC-SGD is superior to previous works in either the convergence rate or the communication cost, which indicates that LIEC-SGD could inherit the dual advantages from unidirectional compression and bidirectional compression. Finally, experiments of training deep neural networks validate the effectiveness of the proposed LIEC-SGD algorithm.

Jiadong Xiao, Lin Li, Tie Zhang et al.

In pursuit of the time-optimal path tracking (TOPT) trajectory of a robot manipulator along a preset path, a beforehand identified robot dynamic model is usually used to obtain the required optimal trajectory for perfect tracking. However, due to the inevitable model-plant mismatch, there may be a big error between the actually measured torques and the calculated torques by the dynamic model, which causes the obtained trajectory to be suboptimal or even be infeasible by exceeding given limits. This paper presents a TOPT-oriented SARSA algorithm (TOPTO-SARSA) and a two-step method for finding the time-optimal motion and ensuring the feasibility : Firstly, using TOPTO-SARSA to find a safe trajectory that satisfies the kinematic constraints through the interaction between reinforcement learning agent and kinematic model. Secondly, using TOPTO-SARSA to find the optimal trajectory through the interaction between the agent and the real world, and assure the actually measured torques satisfy the given limits at the last interaction. The effectiveness of the proposed algorithm has been verified through experiments on a 6-DOF robot manipulator.

Jiadong Xiao, Lin Li, Yanbiao Zou et al.

Time-optimal path tracking, as a significant tool for industrial robots, has attracted the attention of numerous researchers. In most time-optimal path tracking problems, the actuator torque constraints are assumed to be conservative, which ignores the motor characteristic; i.e., the actuator torque constraints are velocity-dependent, and the relationship between torque and velocity is piecewise linear. However, considering that the motor characteristics increase the solving difficulty, in this study, an improved Q-learning algorithm for robotic time-optimal path tracking using prior knowledge is proposed. After considering the limitations of the Q-learning algorithm, an improved action-value function is proposed to improve the convergence rate. The proposed algorithms use the idea of reward and penalty, rewarding the actions that satisfy constraint conditions and penalizing the actions that break constraint conditions, to finally obtain a time-optimal trajectory that satisfies the constraint conditions. The effectiveness of the algorithms is verified by experiments.

Hongdiao Wen, Rongjian Xu, Tie Zhang

Our team participate in the challenge of Task 1: Lesion Boundary Segmentation , and use a combined network, one of which is designed by ourselves named updcnn net and another is an improved VGG 16-layer net. Updcnn net uses reduced size images for training, and VGG 16-layer net utilizes large size images. Image enhancement is used to get a richer data set. We use boxes in the VGG 16-layer net network for local attention regularization to fine-tune the loss function, which can increase the number of training data, and also make the model more robust. In the test, the model is used for joint testing and achieves good results.