  Correlations between moments of different flow coefficients are measured in
Pb-Pb collisions at $\sqrt{s_{\rm NN}} = 5.02$ TeV recorded with the ALICE
detector. These new measurements are based on multiparticle mixed harmonic
cumulants calculated using charged particles in the pseudorapidity region
$|\eta|<0.8$ with the transverse momentum range $0.2 < p_{\rm T} < 5.0$
GeV/$c$. The centrality dependence of correlations between two flow
coefficients as well as the correlations between three flow coefficients, both
in terms of their second moments, are shown. In addition, a collection of mixed
harmonic cumulants involving higher moments of $v_2$ and $v_3$ is measured for
the first time, where the characteristic signature of negative, positive and
negative signs of four-, six- and eight-particle cumulants are observed,
respectively. The measurements are compared to the hydrodynamic calculations
using iEBE-VISHNU with AMPT and TRENTo initial conditions. It is shown that the
measurements carried out using the LHC Run 2 data in 2015 have the precision to
explore the details of initial-state fluctuations and probe the nonlinear
hydrodynamic response of $v_2$ and $v_3$ to their corresponding initial
anisotropy coefficients $\varepsilon_2$ and $\varepsilon_3$. These new studies
on correlations between three flow coefficients as well as correlations between
higher moments of two different flow coefficients will pave the way to tighten
constraints on initial-state models and help to extract precise information on
the dynamic evolution of the hot and dense matter created in heavy-ion
collisions at the LHC.
