The main goal of mechanics is finding solutions for important variables of interest, from which every other dynamical variable can be easily computed. In fluid mechanics, the main objective for a given problem is finding a velocity field (once you have this, you&#x27;re done). Since the NS equations are non-linear partial differential equations, finding exact solutions is impossible in most cases. Some notable non-trivial exceptions exist [1]. Navier-Stokes is extremely successful in describing flows in many real physical situations. It is believed, but has not been experimentally confirmed, that Navier-Stokes successfully describes turbulent flow. Most physical theories have a fairly well known domain in which they are applicable and not applicable (Newtonian physics breaks down at velocities near the speed of light). Currently, we don&#x27;t even know if solutions to NS always exist, never mind make physical sense [2]. With this in mind, we have to acknowledge the uncertainty of the correctness of NS in describing <i>an arbitrary flow</i>. It is backed by well-grounded theory (parts of the equations can be derived from conservation laws) and works under many different conditions. This comment landed up longer than I expected, but my main point is that the question can we &quot;reliably simulate fluid behavior&quot; for an arbitrary fluid - is largely up in the air [3].<p>However, we should restrict our attention to flows that we very strongly believe are correctly described by NS. From the original paper:<p>&gt;&gt; The main problem of our method is the same as the weakness of all machine learning approaches; the learning methods are not capable to extrapolate the model far outside the data observed during training.<p>The training data are existing numerical simulations of specific fluid flows. The learning algorithm <i>learned fluid flow dynamics</i> from simulations. This is extremely impressive. It also achieves a significant speed up in simulation time - which is also very impressive. However, as the authors say, it does not generalise well. So, in short the answer to your first question is probably &quot;sometimes yes, but in general not really&quot;.<p>edit: I should add that the simulations in the paper are decidedly based on Navier-Stokes.<p>[1] <a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Hagen%E2%80%93Poiseuille_flow_from_the_Navier%E2%80%93Stokes_equations" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Hagen%E2%80%93Poiseuille_flow_...</a><p>[2] <a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Navier%E2%80%93Stokes_existence_and_smoothness" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Navier%E2%80%93Stokes_existenc...</a><p>[3] <a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Turbulence" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Turbulence</a>