Porous-DeepONet: Learning the Solution Operators of Parametric Reactive Transport Equations in Porous Media

Abstract

Reactive transport equations in porous media are critical in various scientific and engineering disciplines, but solving these equations can be computationally expensive when exploring different scenarios, such as varying porous structures and initial or boundary conditions. The deep operator network (DeepONet) has emerged as a popular deep learning framework for solving parametric partial differential equations. However, applying the DeepONet to porous media presents significant challenges due to its limited capability to extract representative features from intricate structures. To address this issue, we propose the Porous-DeepONet, a simple yet highly effective extension of the DeepONet framework that leverages convolutional neural networks (CNNs) to learn the solution operators of parametric reactive transport equations in porous media. By incorporating CNNs, we can effectively capture the intricate features of porous media, enabling accurate and efficient learning of the solution operators. We demonstrate the effectiveness of the Porous-DeepONet in accurately and rapidly learning the solution operators of parametric reactive transport equations with various boundary conditions, multiple phases, and multi-physical fields through five examples. This approach offers significant computational savings, potentially reducing the computation time by 50–1000 times compared with the finite-element method. Our work may provide a robust alternative for solving parametric reactive transport equations in porous media, paving the way for exploring complex phenomena in porous media.