Deep Recurrent Neural Network Architecture of High Order Indirect Integration Method - Xie, Zhengrong; Ai, Yibo; Chen, Jia; Wang, Fan; Zhang, Weidong (Neural processing letters, 2022)
The indirect integration method (IIM) is a numerical method for initial value problem of ordinary differential equation, which is based on the residual iteration of differential equation to optimize the parameters of the highest order derivative function layer, and then integrates to the solution function layer step by step through complex trapezoid quadrature formula. Considering the recurrence format of IIM, a single-layer recurrent neural network is first designed to simulate the first-order IIM; On this basis, a deep recurrent neural network is constructed by stacking single-layer recurrent networks to implement any order IIM algorithm; Taking the structure of deep RNN as the calculation diagram, the error back-propagation paths are graded according to the order of traversal differential state and with the help of BPTT algorithm, the recursive relationship between the path parameter gradients (equivalent to the parameter gradients of different order IIM) is obtained.