Learning generic solutions for multiphase transport in porous media via the flux functions operator

Waleed Diab, Omar Chaabi, Shayma Alkobaisi, Abeeb Awotunde, Mohammed Al Kobaisi*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Traditional numerical schemes for simulating multiphase flow and transport in porous media can be computationally expensive, and continues to be an active area of research. Advances in machine learning for scientific computing have the potential to help speed up the simulation time in many scientific and engineering fields. DeepONet has recently emerged as a powerful tool for accelerating the solution of partial differential equations (PDEs) by learning operators (mapping between function spaces) of PDEs. In this work, we learn the mapping between the space of flux functions of the Buckley-Leverett PDE and the space of solutions (saturations). We use Physics-Informed DeepONets (PI-DeepONets) to achieve this mapping without any paired input-output observations, except for a set of given initial or boundary conditions; ergo, eliminating the expensive data generation process. By leveraging the underlying physical laws via soft penalty constraints during model training, in a manner similar to Physics-Informed Neural Networks (PINNs), and a unique deep neural network architecture, the proposed PI-DeepONet model can predict the solution accurately given any type of flux function (concave, convex, or non-convex) while achieving up to four orders of magnitude improvements in speed over traditional numerical solvers. Moreover, the trained PI-DeepONet model demonstrates excellent generalization qualities, rendering it a promising tool for accelerating the solution of transport problems in porous media.

Original languageEnglish
Article number104609
JournalAdvances in Water Resources
StatePublished - Jan 2024

Bibliographical note

Publisher Copyright:
© 2023 The Author(s)


  • Buckley-leverett
  • Deep neural networks
  • Machine learning
  • Operator learning
  • Transport in porous media

ASJC Scopus subject areas

  • Water Science and Technology


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