用图神经网络模拟断裂多孔介质中的流体运移,提升预测精度与泛化能力。
Learning multi-phase flow and transport in fractured porous media with auto-regressive and recurrent graph neural networks
- 基于EDFM网格构建图神经网络,捕捉断裂介质复杂拓扑结构
- 两阶段训练有效减少自回归推理时的误差累积,饱和与压力预测准确
- 循环GNN在长序列预测上表现更优,适合动态过程长期推演
过去三十年来,针对断裂多孔介质中多相流与运移过程的建模,已发展出多种计算方法与仿真框架。一致对齐裂缝表面的共形网格方法虽精度高,但需精细网格划分,难以应用于大规模或复杂裂缝网络。本文提出使用图神经网络(GNN)学习此类复杂动态过程。由于嵌入式离散裂缝模型(EDFM)产生的计算网格具有非结构化拓扑,十分适合采用GNN建模。本文设计两种深度学习架构:标准GNN与循环GNN。两者均采用两阶段训练策略:先进行自回归单步滚动训练,再通过全序列真实数据监督进行微调。实验表明,该策略有效缓解了测试阶段自回归推理中的误差累积问题。两种模型均能良好泛化至未见裂缝构型,饱和序列预测性能相当,循环GNN在压力序列预测上略优。第二阶段训练对标准GNN有益,但对循环GNN影响较小。此外,测试了两种模型的时间外推能力,循环GNN在长期序列预测中显著优于标准GNN,凸显其对长时间动态过程的建模优势。
原文摘要 · Abstract (English)
In the past three decades, a wide array of computational methodologies and simulation frameworks has emerged to address the complexities of modeling multi-phase flow and transport processes in fractured porous media. The conformal mesh approaches which explicitly align the computational grid with fracture surfaces are considered by many to be the most accurate. However, such methods require excessive fine-scale meshing, rendering them impractical for large or complex fracture networks. In this work, we propose to learn the complex multi-phase flow and transport dynamics in fractured porous media with graph neural networks (GNN). GNNs are well suited for this task due to the unstructured topology of the computation grid resulting from the Embedded Discrete Fracture Model (EDFM) discretization. We propose two deep learning architectures, a GNN and a recurrent GNN. Both networks follow a two-stage training strategy: an autoregressive one step roll-out, followed by a fine-tuning step where the model is supervised using the whole ground-truth sequence. We demonstrate that the two-stage training approach is effective in mitigating error accumulation during autoregressive model rollouts in the testing phase. Our findings indicate that both GNNs generalize well to unseen fracture realizations, with comparable performance in forecasting saturation sequences, and slightly better performance for the recurrent GNN in predicting pressure sequences. While the second stage of training proved to be beneficial for the GNN model, its impact on the recurrent GNN model was less pronounced. Finally, the performance of both GNNs for temporal extrapolation is tested. The recurrent GNN significantly outperformed the GNN in terms of accuracy, thereby underscoring its superior capability in predicting long sequences.
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