Fourier Neural Operator for Fluid Flow in Small-Shape 2D Simulated Porous Media Dataset

Abouzar Choubineh*, Jie Chen*, David A. Wood, Frans Coenen, Fei Ma

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


Machine Learning (ML) and/or Deep Learning (DL) methods can be used to predict fluid flow in porous media, as a suitable replacement for classical numerical approaches. Such data-driven approaches attempt to learn mappings between finite-dimensional Euclidean spaces. A novel neural framework, named Fourier Neural Operator (FNO), has been recently developed to act on infinite-dimensional spaces. A high proportion of the research available on the FNO has focused on problems with large-shape data. Furthermore, most published studies apply the FNO method to existing datasets. This paper applies and evaluates FNO to predict pressure distribution over a small, specified shape-data problem using 1700 Finite Element Method (FEM) generated samples, from heterogeneous permeability fields as the input. Considering FEM-calculated outputs as the true values, the configured FNO model provides superior prediction performance to that of a Convolutional Neural Network (CNN) in terms of statistical error assessment based on the coefficient of determination (R (Formula presented.)) and Mean Squared Error (MSE). Sensitivity analysis considering a range of FNO configurations reveals that the most accurate model is obtained using (Formula presented.) and (Formula presented.). Graphically, the FNO model precisely follows the observed trend in each porous medium evaluated. There is potential to further improve the FNO’s performance by including physics constraints in its network configuration.

Original languageEnglish
Article number24
Issue number1
Publication statusPublished - Jan 2023


  • convolutional neural network
  • finite element method
  • Fourier neural operator
  • sensitivity analysis
  • small-shape data
  • subsurface fluid flow


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