In this study, we prove rigourous bounds on the error and stability analysis of deep learning methods for the nonstationary Magneto-hydrodynamics equations. We obtain the approximate ability of the neural network by the convergence of a loss function and the convergence of a Deep Neural Network (DNN) to the exact solution. Moreover, we derive explicit error estimates for the solution computed by optimizing the loss function in the DNN approximation of the solution.

翻译：本研究对非平稳磁流体动力学方程的深度学习方法的误差和稳定性分析给出了严格的理论界。通过损失函数的收敛性以及深度神经网络（DNN）向精确解的收敛性，我们获得了神经网络的近似能力。此外，我们还在DNN求解近似过程中，通过对损失函数进行优化所得到的解，推导出了明确的误差估计。