The Application Of Support Vector Machine In Boundary Probleme

Support Vector Machine is a new method of machine learning. It has become one research focus in the field of international Machine Learning. Support Vector Regression is an important branch of SVM. because of its excellent learning capacity and generalizing ability, it has been applied to many fields, for example: image segmentation, system prediction, estimating parameter and good results have been gained.The boundary problem of differential equations is a problem of function regression. We have solve the problems which have Dirichlet BC, Neuman BC and mixed BC. Moreover, we have solve boundary value problems with irregular boundary and several medias by SVM. When we solve irregular problem, a trial solution of the differential equation is written as a sum of two parts: a radial basis function network satisfies the boundary conditions and SVR is trained for the inner points. When we solve the several medias problem, the medias' coefficient is constant. So we can solve the problem in each several fields. We can divide the field into several small areas, and the medium coefficients are constant and different in each small areas .For the no_linear case, the kernel_function K(x,y) = (Φ(x).Φ(y))maps the data from the input space to characteristic space. In the cause of training, we note that the kernel_function is choosing according to the problem. The polynomial and RBF kernel_function are in common use. The proper choice of the kernel_function affects the precision and the error rate of the learning.