  The Fourier neural operator (FNO) framework is applied to the large eddy
simulation (LES) of three-dimensional compressible Rayleigh-Taylor (RT)
turbulence with miscible fluids at Atwood number $A_t=0.5$, stratification
parameter $Sr=1.0$, and Reynolds numbers $Re=10000$ and 30000. The FNO model is
first used for predicting three-dimensional compressible turbulence. The
different magnitudes of physical fields are normalized using root mean square
values for an easier training of FNO models. In the \emph{a posteriori} tests,
the FNO model outperforms the velocity gradient model (VGM), the dynamic
Smagorinsky model (DSM), and implicit large eddy simulation (ILES) in
predicting various statistical quantities and instantaneous structures, and is
particularly superior to traditional LES methods in predicting temperature
fields and velocity divergence. Moreover, the computational efficiency of the
FNO model is much higher than that of traditional LES methods. FNO models
trained with short-time, low Reynolds number data exhibit a good generalization
performance on longer-time predictions and higher Reynolds numbers in the
\emph{a posteriori} tests.
