Skip to main content

Inference of Differential Equations for Modeling Chemical Reactions

  • Conference paper
Advances in Neural Networks – ISNN 2009 (ISNN 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5551))

Included in the following conference series:

Abstract

This paper presents an evolutionary method for identifying a system of ordinary differential equations (ODEs) from the observed time series data. The structure of ODE is inferred by the Multi Expression Programming (MEP) and the ODE’s parameters are optimized by using particle swarm optimization (PSO). The experimental results on chemical reaction modeling problems show effectiveness of the proposed method.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Tsoulos, I.G., Lagaris, I.E.: Solving Differential Equations with Genetic Programming. Genetic Programming and Evolvable Machines 1, 1389–2576 (2006)

    Google Scholar 

  2. Cao, H., Kang, L., Chen, Y., Yu, J.: Evolutionary Modeling of Systems of Ordinary Differential Equations with Genetic Programming. Genetic Programming and Evolvable Machines 40, 309–337 (2000)

    Article  MATH  Google Scholar 

  3. Iba, H., Mimura, A.: Inference of a Gene Regulatory Network by Means of Interactive Evolutionary Computing. Information Sciences 145, 225–236 (2002)

    Article  Google Scholar 

  4. Bongard, J., Lipson, H.: Automated Reverse Engineering of Nonlinear Dynamical Systems. Proceedings of the National Academy of Science 104, 9943–9948 (2007)

    Article  MATH  Google Scholar 

  5. Oltean, M., Dumitrescu, D.: Multi Expression Programming. Technical Report, UBB-01-2002, Babes-Bolyai University, Cluj-Napoca, Romania, www.mep.cs.ubbcluj.rog

  6. Crina, G., Ajith, A., Sang, Y.H.: Multi-Expression Programming for Intrusion Detection System. In: Mira, J., Álvarez, J.R. (eds.) IWINAC 2005. LNCS, vol. 3562, pp. 163–172. Springer, Heidelberg (2005)

    Google Scholar 

  7. Andrew, H.W.: System Identification Using Genetic Programming. In: Proc. of 2nd Int. Conference on Adaptive Computing in Engineering Design and Control (1996)

    Google Scholar 

  8. Oltean, M., Grosan, C.: Evolving Digital Circuits Using Multi Expression Programming. In: Zebulum, R., et al. (eds.) NASA/DoD Conference on Evolvable Hardware, Seattle, June 24-26, pp. 87–90. IEEE Press, NJ (2004)

    Google Scholar 

  9. Chen, Y.H., Yang, B., Ajith, A.: Flexible Neural Trees Ensemble for Stock Index Modeling. Neurocomputing 70, 697–703 (2007)

    Article  Google Scholar 

  10. Takeuchi, Y.: Global Dynamical Properties of Lotka-Volterra Systems. World Scientific, Singapore (1996)

    Book  MATH  Google Scholar 

  11. Arkin, A.P., Ross, J.: Statistical Construction of Chemical Reaction Mechanisms from Measured Time-Series. J. Phys. Chem., 970–979 (1995)

    Google Scholar 

  12. Gennemark, P., Wedelin, D.: Efficient Algorithms for Ordinary Differential Equation Model Identification of Biological Systems. IET Syst. Biol. 1, 120–129 (2007)

    Article  Google Scholar 

  13. Savageau, M.A.: Biochemical Systems Analysis: A Study of Function and Design in Molecular Biology. Addison-Wesley, Reading (1976)

    MATH  Google Scholar 

  14. Hitoshi, I.: Inference of Differential Equation Models by Genetic Programming. Information Sciences 178, 4453–4468 (2008)

    Article  Google Scholar 

  15. Mark, G.: Bayesian Inference for Differential Equations. Theoretical Computer Science 408, 4–16 (2008)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Yang, B., Chen, Y., Meng, Q. (2009). Inference of Differential Equations for Modeling Chemical Reactions. In: Yu, W., He, H., Zhang, N. (eds) Advances in Neural Networks – ISNN 2009. ISNN 2009. Lecture Notes in Computer Science, vol 5551. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01507-6_114

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-01507-6_114

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-01506-9

  • Online ISBN: 978-3-642-01507-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics