Xiaoli Wang

Housen Wang, Yuxing Chen, Sirong Cao et al.

We propose a unified framework for delay differential equations (DDEs) based on deep neural networks (DNNs) - the neural delay differential equations (NDDEs), aimed at solving the forward and inverse problems of delay differential equations. This framework could embed delay differential equations into neural networks to accommodate the diverse requirements of DDEs in terms of initial conditions, control equations, and known data. NDDEs adjust the network parameters through automatic differentiation and optimization algorithms to minimize the loss function, thereby obtaining numerical solutions to the delay differential equations without the grid dependence and polynomial interpolation typical of traditional numerical methods. In addressing inverse problems, the NDDE framework can utilize observational data to perform precise estimation of single or multiple delay parameters, which is very important in practical mathematical modeling. The results of multiple numerical experiments have shown that NDDEs demonstrate high precision in both forward and inverse problems, proving their effectiveness and promising potential in dealing with delayed differential equation issues.

Miao Ye, Hongwen Hu, Xiaoli Wang et al.

The cross-domain multicast routing problem in a software-defined wireless network with multiple controllers is a classic NP-hard optimization problem. As the network size increases, designing and implementing cross-domain multicast routing paths in the network requires not only designing efficient solution algorithms to obtain the optimal cross-domain multicast tree but also ensuring the timely and flexible acquisition and maintenance of global network state information. However, existing solutions have a limited ability to sense the network traffic state, affecting the quality of service of multicast services. In addition, these methods have difficulty adapting to the highly dynamically changing network states and have slow convergence speeds. To this end, this paper aims to design and implement a multiagent deep reinforcement learning based cross-domain multicast routing method for SDWN with multicontroller domains. First, a multicontroller communication mechanism and a multicast group management module are designed to transfer and synchronize network information between different control domains of the SDWN, thus effectively managing the joining and classification of members in the cross-domain multicast group. Second, a theoretical analysis and proof show that the optimal cross-domain multicast tree includes an interdomain multicast tree and an intradomain multicast tree. An agent is established for each controller, and a cooperation mechanism between multiple agents is designed to effectively optimize cross-domain multicast routing and ensure consistency and validity in the representation of network state information for cross-domain multicast routing decisions. Third, a multiagent reinforcement learning-based method that combines online and offline training is designed to reduce the dependence on the real-time environment and increase the convergence speed of multiple agents.