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

1$\begingroup$ Crossposted: cs.stackexchange.com/q/88698/755, mathoverflow.net/q/294017. Please do not post the same question on multiple sites. Each community should have an honest shot at answering without anybody's time being wasted. $\endgroup$ – D.W. Feb 28 '18 at 4:46
One of the earliest papers is Application of machine learning algorithms to flow modeling and optimization (1999).
A model reduction can be accomplished by projecting the NavierStokes equations on a properly selected lower dimensional phase subspace. A reasonable choice for a “proper” selection criterion for the base of this manifold is the maximization of the energy content of the projection. This operation is called Proper Orthogonal Decomposition (POD), or Linear Principal Components Analysis (PCA).
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 multilayer feedforward neural network.
For more recent work, see