Combining first principles modelling and artificial neural networks: A general framework

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Biochemical processes involving cellular catalysis are usually very difficult to model accurately essentially due to the inherent complexity of the intracellular phenomena as well as the population heterogeneity. When processes are complex and poorly understood in a mechanistic sense, hybrid modelling through knowledge integration can be employed with advantage because the model accuracy can be increased by the incorporation of alternative and complementary sources of knowledge. In this work a bioreactor dynamical hybrid model is proposed that combines first principles modelling with artificial neural networks (ANNs): the bioreactor system is described by a set of mass balance equations, and the cell population system is represented by an adjustable mixture of neural network and mechanistic representations. Bounded input bounded output (BIBO) stability conditions are derived for the general dynamic hybrid model. Two strategies for the identification of embedded neural networks are compared. The sensitivities equations are derived enabling the analytical calculation of the Jacobian matrix. The application of the theory is illustrated with two simulation case studies.

Original languageEnglish
Pages (from-to)755-766
Number of pages12
JournalComputers and Chemical Engineering
Issue number5
Publication statusPublished - 15 May 2004


  • Artificial neural networks
  • Bioprocesses
  • Dynamical modelling
  • Hybrid modelling
  • Stability


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