Modeling of complex dynamic systems using differential neural networks with the incorporation of a priori knowledge

Fethi Bellamine, A. Almansoori, Ali ElKamel

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


In this paper, neural algorithms, including the multi-layered perceptron (MLP) differential approximator, generalized hybrid power series, discrete Hopfield neural network, and the hybrid numerical, are used for constructing models that incorporate a priori knowledge in the form of differential equations for dynamic engineering processes. The properties of these approaches are discussed and compared to each other in terms of efficiency and accuracy. The presented algorithms have a number of advantages over other traditional mesh-based methods such as reduction of the computational cost, speed up of the execution time, and data integration with the a priori knowledge. Furthermore, the presented techniques are applicable when the differential equations governing a system or dynamic engineering process are not fully understood. The proposed algorithms learn to compute the unknown or free parameters of the equation from observations of the process behavior, hence a more precise theoretical description of the process is obtained. Additionally, there will be no need to solve the differential equation each time the free parameters change. The parallel nature of the approaches outlined in this paper make them attractive for parallel implementation in dynamic engineering processes.

Original languageBritish English
Pages (from-to)515-526
Number of pages12
JournalApplied Mathematics and Computation
StatePublished - 13 Jun 2015


  • A priori knowledge
  • Control system studies
  • Dynamic systems
  • Engineering processes
  • Neural networks


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