Robin Pre-Training for the Deep Ritz Method

Published: 01 Jan 2023, Last Modified: 15 May 2025NLDL 2023EveryoneRevisionsBibTeXCC BY-SA 4.0
Abstract: 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.
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