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.

中文翻译：

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Porous-DeepONet：学习多孔介质中参数反应输运方程的解算子


多孔介质中的反应输运方程在各种科学和工程学科中都至关重要，但在探索不同的场景（例如变化的多孔结构和初始或边界条件）时，求解这些方程的计算成本可能很高。深度算子网络（DeepONet）已成为解决参数偏微分方程的流行深度学习框架。然而，由于 DeepONet 从复杂结构中提取代表性特征的能力有限，因此将 DeepONet 应用于多孔介质面临着重大挑战。为了解决这个问题，我们提出了 Porous-DeepONet，这是 DeepONet 框架的简单而高效的扩展，它利用卷积神经网络（CNN）来学习多孔介质中参数反应输运方程的解算子。通过结合 CNN，我们可以有效地捕获多孔介质的复杂特征，从而能够准确、高效地学习解算子。我们通过五个例子证明了 Porous-DeepONet 在准确、快速地学习具有各种边界条件、多相和多物理场的参数反应输运方程的解算子方面的有效性。这种方法可显着节省计算量，与有限元方法相比，计算时间可能减少 50-1000 倍。我们的工作可能为求解多孔介质中的参数反应输运方程提供可靠的替代方案，为探索多孔介质中的复杂现象铺平道路。