We provide convergence guarantees for the Deep Ritz Method for abstract variational energies. Our results cover non-linear variational problems such as the $p$-Laplace equation or the Modica-Mortola energy with essential or natural boundary conditions. Under additional assumptions, we show that the convergence is uniform across % bounded families of right-hand sides.

翻译：我们为深丽兹方法的抽象变异能量提供了趋同保证。我们的结果涵盖了非线性变异问题,如美元-拉普尔方程或具有基本或自然边界条件的摩尔托拉-摩尔托拉能源。 在其他假设下,我们表明,这种趋同在右侧受约束的家庭中是统一的。