论文标题
椭圆形PDE的深层混合残留方法的先验误差估计值
Priori Error Estimate of Deep Mixed Residual Method for Elliptic PDEs
论文作者
论文摘要
在这项工作中，我们在求解某些椭圆PDE时得出了混合残差方法的先验误差估计。我们的工作是该方法的第一个理论研究。我们证明，如果我们增加训练样本和网络大小，而没有任何限制训练样本与网络大小的限制，则神经网络解决方案将融合。此外，我们的结果表明，混合剩余方法可以比Deep Ritz方法更好地恢复高阶衍生物，而Deep Ritz方法也通过我们的数值实验验证了。
In this work, we derive a priori error estimate of the mixed residual method when solving some elliptic PDEs. Our work is the first theoretical study of this method. We prove that the neural network solutions will converge if we increase the training samples and network size without any constraint on the ratio of training samples to the network size. Besides, our results suggest that the mixed residual method can recover high order derivatives better than the deep Ritz method, which has also been verified by our numerical experiments.
