论文标题
物理知情的错误估计近似于Navier-Stokes方程的神经网络
Error estimates for physics informed neural networks approximating the Navier-Stokes equations
论文作者
论文摘要
我们证明，由于不可压缩的Navier-Stokes方程与（扩展）物理学知情的神经网络的近似值所产生的错误。我们表明，对于具有两个隐藏层的Tanh神经网络，可以任意将基础PDE残留物制成。此外，可以根据训练错误，网络大小和正交点的数量来估算总误差。通过数值实验说明了该理论。
We prove rigorous bounds on the errors resulting from the approximation of the incompressible Navier-Stokes equations with (extended) physics informed neural networks. We show that the underlying PDE residual can be made arbitrarily small for tanh neural networks with two hidden layers. Moreover, the total error can be estimated in terms of the training error, network size and number of quadrature points. The theory is illustrated with numerical experiments.
