Neural network approximation to nonlinear dynamics by velocity error backpropagation

Hidenori Ishii, Eitaro Aiyoshi

Research output: Contribution to journalArticlepeer-review


This paper presents a new type of recurrent neural network (RNN) and its learning algorithm for nonlinear dynamics, called "Velocity-Error Backpropagation (VEBP)." In VEBP, learning is performed in two steps: (a) The velocity vector field of reference trajectories is approximated by a feedforward neural network (NN) with biconnection layers by backpropagating the velocity errors directly. (b) The RNN is constructed by adding integrators and output feedback loops to the trained feedforward NN. VEBP has some advantages over "backpropagation through time (BPTT)," the conventional learning method for RNNs. The effectiveness of the presented RNN and its learning algorithm is demonstrated by simulation results for some examples of nonlinear dynamics.

Original languageEnglish
Pages (from-to)26-35
Number of pages10
JournalElectrical Engineering in Japan (English translation of Denki Gakkai Ronbunshi)
Issue number2
Publication statusPublished - 2002 Jul 30


  • Approximation
  • Backpropagation
  • Dynamics
  • Learning algorithm
  • Recurrent neural network

ASJC Scopus subject areas

  • Energy Engineering and Power Technology
  • Electrical and Electronic Engineering


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