  A search for physics beyond the Standard Model inducing periodic signals in
the dielectron and diphoton invariant mass spectra is presented using 139
fb$^{-1}$ of $\sqrt{s}=13$ TeV $pp$ collision data collected by the ATLAS
experiment at the LHC. Novel search techniques based on continuous wavelet
transforms are used to infer the frequency of periodic signals from the
invariant mass spectra and neural network classifiers are used to enhance the
sensitivity to periodic resonances. In the absence of a signal, exclusion
limits are placed at the 95\% confidence level in the two-dimensional parameter
space of the clockwork gravity model. Model-independent searches for deviations
from the background-only hypothesis are also performed.
