Upscaling models of solute transport in porous media through genetic programming

David J. Hill, Barbara S. Minsker, Albert J. Valocchi, Vladan Babovic, Maarten Keijzer

Research output: Contribution to journalArticlepeer-review


Due to the considerable computational demands of modeling solute transport in heterogeneous porous media, there is a need for upscaled models that do not require explicit resolution of the small-scale heterogeneity. This study investigates the development of upscaled solute transport models using genetic programming (GP), a domain-independent modeling tool that searches the space of mathematical equations for one or more equations that describe a set of training data. An upscaling methodology is developed that facilitates both the GP search and the implementation of the resulting models. A case study is performed that demonstrates this methodology by developing vertically averaged equations of solute transport in perfectly stratified aquifers. The solute flux models developed for the case study were analyzed for parsimony and physical meaning, resulting in an upscaled model of the enhanced spreading of the solute plume, due to aquifer heterogeneity, as a process that changes from predominantly advective to Fickian. This case study not only demonstrates the use and efficacy of GP as a tool for developing upscaled solute transport models, but it also provides insight into how to approach more realistic multi-dimensional problems with this methodology.

Original languageEnglish (US)
Pages (from-to)251-266
Number of pages16
JournalJournal of Hydroinformatics
Issue number4
StatePublished - Oct 2007


  • Data-driven modeling
  • Genetic programming
  • Knowledge discovery
  • Solute transport

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Water Science and Technology
  • Geotechnical Engineering and Engineering Geology
  • Atmospheric Science


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