SVM for solving ordinary and partial differential equations with regular boundary

Support Vector Machine (SVM) is a learning technique based on the structural risk minimization principle, and it is also a class of regression method with a good generalization ability. Support Vector Regression (SVR) is a very important branch of Support Vector Machine. This paper first introduces the base knowledge of Support Vector Regression. Then it illustrates the method capable of dealing with ordinary and partial differential equations with regular boundary (Dirichlet or Neumann) by using SVR. After this, it gives some examples for further explanations. At last, it compares the results of SVM with that of artificial neural networks and explains the reason.