为了实时解决前馈神经网络学习过程中可能遇到的小残量问题和大残量问题,引入QuasiNewton优化算法,并与GaussNewton法相结合,构建基于GaussNewton QuasiNewton法的前馈神经网络.根据每次迭代的结果判断属于大残量问题还是小残量问题,进...为了实时解决前馈神经网络学习过程中可能遇到的小残量问题和大残量问题,引入QuasiNewton优化算法,并与GaussNewton法相结合,构建基于GaussNewton QuasiNewton法的前馈神经网络.根据每次迭代的结果判断属于大残量问题还是小残量问题,进而选择采取GaussNewton迭代步或QuasiNewton迭代步.与基于最速下降法的经典前馈神经网络以及与基于GaussNewton法的前馈神经网络的对比实验表明,所构造的基于Gauss Newton QuasiNewton法的前馈神经网络较好地解决了残量问题,具有良好的收敛性和稳定性.展开更多
In this paper,a level set method is applied to the inverse problem of 2-D wave equation in the fluid-saturated media.We only consider the situation that the parameter to be recovered takes two different values,which l...In this paper,a level set method is applied to the inverse problem of 2-D wave equation in the fluid-saturated media.We only consider the situation that the parameter to be recovered takes two different values,which leads to a shape reconstruction problem.A level set function is used to present the discontinuous parameter,and a regularization functional is applied to the level set function for the ill-posed problem.Then the resulting inverse problem with respect to the level set function is solved by using the damped Gauss-Newton method.Numerical experiments show that the method can recover parameter with complicated geometry and the noise in the observation data.展开更多
文摘为了实时解决前馈神经网络学习过程中可能遇到的小残量问题和大残量问题,引入QuasiNewton优化算法,并与GaussNewton法相结合,构建基于GaussNewton QuasiNewton法的前馈神经网络.根据每次迭代的结果判断属于大残量问题还是小残量问题,进而选择采取GaussNewton迭代步或QuasiNewton迭代步.与基于最速下降法的经典前馈神经网络以及与基于GaussNewton法的前馈神经网络的对比实验表明,所构造的基于Gauss Newton QuasiNewton法的前馈神经网络较好地解决了残量问题,具有良好的收敛性和稳定性.
文摘In this paper,a level set method is applied to the inverse problem of 2-D wave equation in the fluid-saturated media.We only consider the situation that the parameter to be recovered takes two different values,which leads to a shape reconstruction problem.A level set function is used to present the discontinuous parameter,and a regularization functional is applied to the level set function for the ill-posed problem.Then the resulting inverse problem with respect to the level set function is solved by using the damped Gauss-Newton method.Numerical experiments show that the method can recover parameter with complicated geometry and the noise in the observation data.
