四川大学学报（自然科学版）2024，Vol.61Issue(6)：59-70,12.DOI:10.19907/j.0490-6756.2024.062002
DC-DeepONet:一种求解多尺度偏微分方程的算子学习方法
DC-DeepONet:An operator learning method for multiscale differential equations
摘要
Abstract
Various multiscale phenomena,such as turbulence,microstructured materials,and the coupled in-teraction between bubbles and particles,are present in nature.The modeling of these phenomena often uses partial differential equations(PDEs)that exhibit multiscale characteristics.Operator learning,a novel para-digm utilizing deep neural networks for solving PDEs,has shown significant advantages in terms of generaliz-ability and computational efficiency.However,existing operator learning models face challenges in solving multiscale PDEs,particularly with the frequency principle,due to their inability to effectively learn high-frequency signals.To address this issue,our paper introduces two new network models:C-DeepONet and DC-DeepONet,which are based on convolutional neural networks and DeepONet.The two models utilize standard and dilated convolution respectively,specifically designed for addressing multiscale PDEs,enabling effective capture of high-frequency features in multiscale scenarios.Experiments are performed using multi-scale Poisson equations and Darcy flow equations as illustrative examples.The results demonstrate that the proposed DC-DeepONet achieves an 88%reduction in average relative error compared to the baseline DeepONet model.关键词
算子学习/多尺度/偏微分方程/空洞卷积Key words
Operator learning/Multiscale/Partial differential equations/Dilated convolution分类
信息技术与安全科学引用本文复制引用
汪璐,邹舒帆,邓小刚..DC-DeepONet:一种求解多尺度偏微分方程的算子学习方法[J].四川大学学报（自然科学版）,2024,61(6):59-70,12.基金项目
国家重大专项(GJXM92579) （GJXM92579）
四川省科技计划资助(2023YFG0329) （2023YFG0329）
