Robin Pre-Training for the Deep Ritz Method

We analyze the training process of the Deep Ritz Method for elliptic equations with Dirichlet boundary conditions and highlight problems arising from essential boundary values. Typically, one employs a penalty approach to enforce essential boundary conditions, however, the naive approach to this problem becomes unstable for large penalizations. A novel method to compensate this problem is proposed, using a small penalization strength to pre-train the model before the main training on the target penalization strength is conducted. We present numerical evidence that the proposed method is beneficial.