  Recent years have seen a surge in interest for leveraging neural networks to
parameterize small-scale or fast processes in climate and turbulence models. In
this short paper, we point out two fundamental issues in this endeavor. The
first concerns the difficulties neural networks may experience in capturing
rare events due to limitations in how data is sampled. The second arises from
the inherent multiscale nature of these systems. They combine high-frequency
components (like inertia-gravity waves) with slower, evolving processes
(geostrophic motion). This multiscale nature creates a significant hurdle for
neural network closures. To illustrate these challenges, we focus on the
atmospheric 1980 Lorenz model, a simplified version of the Primitive Equations
that drive climate models. This model serves as a compelling example because it
captures the essence of these difficulties.
