  We apply physics-informed neural networks to three-dimensional
Rayleigh-B\'enard convection in a cubic cell with a Rayleigh number of Ra =
10^6 and a Prandtl number of Pr = 0.7 to assimilate the velocity vector field
from given temperature fields and vice versa. With the respective ground truth
data provided by a direct numerical simulation, we are able to evaluate the
performance of the different activation functions applied (sine, hyperbolic
tangent and exponential linear unit) and different numbers of neurons (32, 64,
128, 256) for each of the five hidden layers of the multi-layer perceptron. The
main result is that the use of a periodic activation function (sine) typically
benefits the assimilation performance in terms of the analyzed metrics,
correlation with the ground truth and mean average error. The higher quality of
results from sine-activated physics-informed neural networks is also manifested
in the probability density function and power spectra of the inferred velocity
or temperature fields. Regarding the two assimilation directions, the
assimilation of temperature fields based on velocities appears to be more
challenging in the sense that it exhibits a sharper limit on the number of
neurons below which viable assimilation results can not be achieved.
