Skip to main content

Proposal and Preliminary Investigation of a Fitness Function for Partial Differential Models

  • Conference paper
  • First Online:
Book cover Genetic Programming (EuroGP 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9025))

Included in the following conference series:

  • 931 Accesses

Abstract

This work proposes and presents a preliminary investigation of a fitness evaluation scheme supported by a proper genotype representation intended to guide an under development expansion to EASEA/EASEA-CLOUD platforms to evolve partial differential equations as models for a specific system of interest, starting with measures from that system. A simple proof of concept using a dynamic bidirectional surface wave is presented, showing that the proposed fitness evaluation scheme is very promising to enable automate system modelling, even when dealing with up to \(\pm 10\,\%\) noise-added data.

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 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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

Notes

  1. 1.

    The number of sub-domains has as an upper bound the number of available points in the dataset.

References

  1. Collet, P., Krüger, F., Maitre, O.: Automatic parallelization of EC on GPGPUs and clusters of GPGPU machines with EASEA and EASEA-CLOUD. In: Tsutsui, S., Collet, P. (eds.) Massively Parallel Evolutionary Computation on GPGPUs. Natural Computing Series, pp. 35–61. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  2. Drazin, P.G.: Nonlinear Systems. Cambridge Texts in Applied Mathematics, Cambridge (1997)

    Google Scholar 

  3. Farlow, S.J.: Partial Differential Equations for Scientists and Engineers. Dover Publications, New York (1993)

    MATH  Google Scholar 

  4. Galerkin, B.G.: Series occuring in various questions concerning the elastic equilibrium of rods and plates. Eng. Bull. (Vestnik Inzhenerov) 19, 897–908 (1915). (in Russian)

    Google Scholar 

  5. Gaucel, S., Keijzer, M., Lutton, E., Tonda, A.: Learning dynamical systems using standard symbolic regression. In: Nicolau, M., Krawiec, K., Heywood, M.I., Castelli, M., García-Sánchez, P., Merelo, J.J., Rivas Santos, V.M., Sim, K. (eds.) EuroGP 2014. LNCS, vol. 8599, pp. 25–36. Springer, Heidelberg (2014)

    Chapter  Google Scholar 

  6. Koza, J.R.: Genetic Programming: On the Programming of Computers by Means of Natural Selection. MIT Press, Cambridge (1992)

    MATH  Google Scholar 

  7. Livermore, P.W., Ierley, G.R.: Quasi-Lp norm orthogonal Galerkin expansions in sums of Jacobi polynomials. Numerical Algorithms 54(4), 533–569 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  8. Luke, Y.L.: The Special Functions and their Approximations. Academic Press, New York (1969)

    MATH  Google Scholar 

  9. Maitre, O.: Genetic programming on GPGPU cards using EASEA. Massively Parallel Evolutionary Computation on GPGPUs. Natural Computing Series, pp. 227–248. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  10. Schmidt, M., Lipson, H.: Distilling free-form natural laws from experimental data. Science 324, 81–85 (2009)

    Article  Google Scholar 

  11. Shen, J., Tang, T., Wang, L.L.: Spectral Methods: Algorithms, Analysis and Applications. Springer, Heidelberg (2011)

    Book  Google Scholar 

  12. Szegö, G.: Orthogonal Polynomials, American Mathematical Society Colloquium Publications, American Mathematical Society, vol. 23, revised edition (1959)

    Google Scholar 

Download references

Acknowledgements

I. S. Peretta would like to thank the non-simultaneous support received from CAPES (PDSE scholarship #18386-12-1) and CNPq (Full PhD scholarship - GD), both Brazilian funding agencies.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Igor S. Peretta .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Peretta, I.S., Yamanaka, K., Bourgine, P., Collet, P. (2015). Proposal and Preliminary Investigation of a Fitness Function for Partial Differential Models. In: Machado, P., et al. Genetic Programming. EuroGP 2015. Lecture Notes in Computer Science(), vol 9025. Springer, Cham. https://doi.org/10.1007/978-3-319-16501-1_15

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-16501-1_15

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-16500-4

  • Online ISBN: 978-3-319-16501-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics