发表机构
Shandong University; China University of Petroleum (East China); Qingdao University of Technology（山东大学; 中国石油大学（华东）; 青岛理工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究提出多分辨率Sobolev学习方法训练傅里叶神经算子，通过引入一阶和二阶梯度损失，提升多孔介质两相达西流跨分辨率代理建模的预测精度。
AI 中文摘要
代理建模对于提高涉及随机参数的物理过程的不确定性量化计算效率至关重要。与传统的代理模型相比，傅里叶神经算子（FNO）的优势在于其跨分辨率预测能力。在本研究中，针对多孔介质中具有随机参数的两相瞬态达西流，构建了基于FNO的跨分辨率代理模型。提出了一种用于FNO的多分辨率Sobolev学习方法，通过在不同分辨率的训练样本的损失函数中引入一阶和二阶梯度，来提高跨分辨率预测的准确性。这些梯度采用与数值模拟网格兼容的、与分辨率相关的有限差分格式进行近似。实验结果表明，新方法在训练FNO以构建跨分辨率代理模型方面是有效的。
英文摘要
Surrogate modelling is important to enhance the computational efficiency of uncertainty quantification for physical processes involving random parameters. The advantage of Fourier neural operator (FNO) compared to conventional surrogates is its cross-resolution prediction capability. In the current study, a cross-resolution surrogate based on FNO is built for two-phase transient Darcy flows in porous media with random parameters. A multiresolution Sobolev learning method is proposed for FNO to enhance the cross-resolution prediction accuracy by incorporating first and second-order gradients in the loss function using training samples of different resolutions. The gradients are approximated by resolution-related finite difference schemes compatible with the grid for numerical simulation. Experimental results demonstrate the effectiveness of the new method in training FNO for building cross-resolution surrogates.
