Numerical simulations of geophysical and atmospheric flows have to rely on
parameterizations of subgrid scale processes due to their limited spatial
resolution. Despite substantial progress in developing parameterization (or
closure) models for subgrid scale (SGS) processes using physical insights and
mathematical approximations, they remain imperfect and can lead to inaccurate
predictions. In recent years, machine learning has been successful in
extracting complex patterns from high-resolution spatio-temporal data, leading
to improved parameterization models, and ultimately better coarse grid
prediction. However, the inability to satisfy known physics and poor
generalization hinders the application of these models for real-world problems.
In this work, we propose a frame invariant closure approach to improve the
accuracy and generalizability of deep learning-based subgrid scale closure
models by embedding physical symmetries directly into the structure of the
neural network. Specifically, we utilized specialized layers within the
convolutional neural network in such a way that desired constraints are
theoretically guaranteed without the need for any regularization terms. We
demonstrate our framework for a two-dimensional decaying turbulence test case
mostly characterized by the forward enstrophy cascade. We show that our frame
invariant SGS model (i) accurately predicts the subgrid scale source term, (ii)
respects the physical symmetries such as translation, Galilean, and rotation
invariance, and (iii) is numerically stable when implemented in coarse-grid
simulation with generalization to different initial conditions and Reynolds
number. This work builds a bridge between extensive physics-based theories and
data-driven modeling paradigms, and thus represents a promising step towards
the development of physically consistent data-driven turbulence closure models