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 .
 A: 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 Navier-Stokes
  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 multi-layer feed-forward neural network.

For more recent work, see     


*

*Convolutional
Neural Networks for Steady Flow Approximation (2016)

*Artificial
neural network method for solving the Navier–Stokes equations
(2014)

