四川大学学报（自然科学版）2025，Vol.62Issue(3)：584-590,7.DOI:10.19907/j.0490-6756.240038
融合模型降阶和机器学习的Darcy-Stokes方程快速求解法
A fast method for Darcy-Stokes equation combing model order reduction and machine learning
摘要
Abstract
Darcy-Stokes equation is a parameterized partial differential equation.Traditionally,the high-precision full-model finite element method is utilized to solve the equation.In practical applications,the Darcy-Stokes equation is required to be simulated repeatedly with different parameters.In these situations,us-ing the high-precision full-model each time is too costly.In this paper,a fast method combing the model order reduction and the machine learning methods is proposed for solving the singular perturbation Darcy-Stokes equation.Firstly,the proper orthogonal decomposition(POD)method is used to construct a low dimensional approximation space of the solution manifold and the reduced order model is obtained.Secondly,to overcome the disadvantage that the model order reduction method needs to modify the full-model,a trained random for-est model is used to obtain the functional relationship between the low dimensional space representation coeffi-cients and the model parameters.Finally,numerical examples are used to show the performance of the method.It is shown that this method can keep the advantages of model order reduction and machine learning methods simultaneously.In comparison with the full-model method,this method improves the computational speed by more than 80 times while ensuring the same computational accuracy.关键词
Darcy-Stokes方程/模型降阶/本征正交分解/机器学习/随机森林Key words
Darcy-Stokes equation/Model order reduction/POD/Machine learning/Random forest分类
数理科学引用本文复制引用
张沁逸,胡奇晓,王皓,张世全..融合模型降阶和机器学习的Darcy-Stokes方程快速求解法[J].四川大学学报（自然科学版）,2025,62(3):584-590,7.基金项目
四川省自然科学基金(2023NSFSC0075) （2023NSFSC0075）
