Random Basis Function Network for Solving Obstacle Problem

Due to the increasing use of deep learning in science and engineering, as well as the ability to solve computational problems, in this talk, we consider the preliminary approach of neural network to solve obstacle problem [1]. By introducing penalty terms [2], we formulate the obstacle problem as a L1 optimization problem and utilize the ability of random basis function network to approximate the solution. The convergence analysis is established into two parts: statistical error and optimization error. The statistical error is estimated by the number of samples while optimization error is reflected in the empirical loss term. Because of supervised-learning and mesh-less advantages, preliminary numerical experiments illustrate the effectiveness of method and verify the variational formulation of obstacle problem.