A Deep Learning Method for Elliptic Hemivariational Inequalities

Deep learning method for solving elliptic hemivariational inequalities is constructed. Using a variational formulation of the corresponding inequality, we reduce it to an unconstrained expectation minimization problem and solve the last one by a stochastic optimization algorithm. The method is applied to a frictional bilateral contact problem and to a frictionless normal compliance contact problem. Numerical experiments show that for fine meshes, the method approximates the solution with accuracy similar to the virtual element method. Besides, the use of local adaptive activation functions improves accuracy and has almost the same computational cost.