# Naviers Stokes equation and machine learning

I am looking for a reference explaining how to solve Navier-Stokes numerically using Machine learning algorithms . Thank you in advance for your help .

The linear POD is an approximation of the flow vector $v$ by a finite expansion of orthonormal functions $\phi_n$ such that: $v = V + > \sum_{i=1}^n a_n(t)\phi_n(x)$, where $V$ is the time averaged flow, $\phi_n$ is the set of the first $n$ eigenvectors of the covariance matrix $C = E[(v_i −V )(v_j −V )]$; when this representation for $v$ is substituted in the Navier Stokes equations, the original PDE model is transformed in an ODE model, composed by n equations. The POD can be expressed as a multi-layer feed-forward neural network.