This paper focuses on discussing Newton’s method and its hybrid with machine learning for the steady state Navier-Stokes Darcy model discretized by mixed element methods.First,a Newton iterative method is introduced ...This paper focuses on discussing Newton’s method and its hybrid with machine learning for the steady state Navier-Stokes Darcy model discretized by mixed element methods.First,a Newton iterative method is introduced for solving the relative discretized problem.It is proved technically that this method converges quadratically with the convergence rate independent of the mixed element mesh size,under certain standard conditions.Later on,a deep learning algorithm is proposed for solving this nonlinear coupled problem.Following the ideas of an earlier work by Huang,Wang and Yang(2020),an Int-Deep algorithm is constructed by combining the previous two methods so as to further improve the computational efficiency and robustness.A series of numerical examples are reported to show the numerical performance of the proposed methods.展开更多
基金partially supported by the China National KeyR&D Project(Grant 2020YFA0709800)the National Natural Science Foundation of China(Grant No.12071289)+1 种基金the Strategic Priority Research Program of the Chinese Academy of Sciences(Grant No.XDA25010402)supported by the National Natural Science Foundation of China(Grant No.12301519).
文摘This paper focuses on discussing Newton’s method and its hybrid with machine learning for the steady state Navier-Stokes Darcy model discretized by mixed element methods.First,a Newton iterative method is introduced for solving the relative discretized problem.It is proved technically that this method converges quadratically with the convergence rate independent of the mixed element mesh size,under certain standard conditions.Later on,a deep learning algorithm is proposed for solving this nonlinear coupled problem.Following the ideas of an earlier work by Huang,Wang and Yang(2020),an Int-Deep algorithm is constructed by combining the previous two methods so as to further improve the computational efficiency and robustness.A series of numerical examples are reported to show the numerical performance of the proposed methods.
