Deep Recurrent Neural Network Architecture of High Order Indirect Integration Method

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 fu...

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Bibliographic Details
Published in:Neural processing letters Vol. 54; no. 2; pp. 1233 - 1253
Main Authors: Xie, Zhengrong, Ai, Yibo, Chen, Jia, Wang, Fan, Zhang, Weidong
Format: Journal Article
Language:English
Published: New York Springer US 01.04.2022
Springer Nature B.V
Subjects:
Algorithms
Approximation
Artificial Intelligence
Back propagation networks
Batch processing
Boundary value problems
Complex Systems
Computational Intelligence
Computer Science
Differential equations
Iterative methods
Motion control
Neural networks
Numerical methods
Optimization
Ordinary differential equations
Parameters
Quadratures
Recurrent neural networks
Deep neural network
Error back propagation algorithm through time
Numerical solution of initial value problem of ODE
Recurrent neural network
Batch processing
Trapezoidal formula of numerical integration
ISSN:1370-4621, 1573-773X
Online Access:Get full text
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Summary: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.
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ISSN:1370-4621
1573-773X
DOI:10.1007/s11063-021-10677-6