论文标题
流体动力学中深度学习方法的错误估计
Error Estimates for Deep Learning Methods in Fluid Dynamics
论文作者
论文摘要
在这项研究中，我们为某些部分偏微分方程（包括不可压缩的Navier-Stokes方程）提供了深度学习技术的错误估计和稳定性分析。特别是，我们通过固定的复杂性在深度神经网络（DNN）近似中优化溶液中的损耗函数来获得明确的误差估计（适用于适当的规范）。
In this study, we provide error estimates and stability analysis of deep learning techniques for certain partial differential equations including the incompressible Navier-Stokes equations. In particular, we obtain explicit error estimates (in suitable norms) for the solution computed by optimizing a loss function in a Deep Neural Network (DNN) approximation of the solution, with a fixed complexity.
