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In this work, we derive a priori error estimate of the mixed residual methodwhen solving some elliptic PDEs. Our work is the first theoretical study ofthis method. We prove that the neural network solutions will converge if weincrease the training samples and network size without any constraint on theratio of training samples to the network size. Besides, our results suggestthat the mixed residual method can recover high order derivatives better thanthe deep Ritz method, which has also been verified by our numericalexperiments.

Priori Error Estimate of Deep Mixed Residual Method for Elliptic PDEs