Diab Waleed, Al Kobaisi Mohammed
Petroleum Engineering Department, Khalifa University of Science and Technology, Abu Dhabi, 127788, UAE.
Sci Rep. 2024 Sep 12;14(1):21298. doi: 10.1038/s41598-024-72393-0.
Learning operators with deep neural networks is an emerging paradigm for scientific computing. Deep Operator Network (DeepONet) is a modular operator learning framework that allows for flexibility in choosing the kind of neural network to be used in the trunk and/or branch of the DeepONet. This is beneficial as it has been shown many times that different types of problems require different kinds of network architectures for effective learning. In this work, we design an efficient neural operator based on the DeepONet architecture. We introduce U-Net enhanced DeepONet (U-DeepONet) for learning the solution operator of highly complex CO-water two-phase flow in heterogeneous porous media. The U-DeepONet is more accurate in predicting gas saturation and pressure buildup than the state-of-the-art U-Net based Fourier Neural Operator (U-FNO) and the Fourier-enhanced Multiple-Input Operator (Fourier-MIONet) trained on the same dataset. Moreover, our U-DeepONet is significantly more efficient in training times than both the U-FNO (more than 18 times faster) and the Fourier-MIONet (more than 5 times faster), while consuming less computational resources. We also show that the U-DeepONet is more data efficient and better at generalization than both the U-FNO and the Fourier-MIONet.
使用深度神经网络学习算子是科学计算中的一种新兴范式。深度算子网络（DeepONet）是一个模块化的算子学习框架，它在选择用于DeepONet主干和/或分支的神经网络类型时具有灵活性。这是有益的，因为多次表明，不同类型的问题需要不同类型的网络架构才能有效学习。在这项工作中，我们基于DeepONet架构设计了一种高效的神经算子。我们引入了U-Net增强的DeepONet（U-DeepONet）来学习非均质多孔介质中高度复杂的CO-水两相流的求解算子。在预测气体饱和度和压力累积方面，U-DeepONet比基于U-Net的最先进的傅里叶神经算子（U-FNO）和在同一数据集上训练的傅里叶增强多输入算子（Fourier-MIONet）更准确。此外，我们的U-DeepONet在训练时间上比U-FNO（快18倍以上）和Fourier-MIONet（快5倍以上）都显著更高效，同时消耗更少的计算资源。我们还表明，U-DeepONet比U-FNO和Fourier-MIONet在数据效率上更高，泛化能力更强。
