We critically examine the ability of future neutrino
telescopes, including Baikal-GVD, KM3NeT, P-ONE, TAMBO, and
IceCube-Gen2, to determine the flavor composition of high-energy
astrophysical neutrinos in light of data from next-generation of
neutrino oscillation experiments including JUNO, DUNE, and
Hyper-Kamiokande. By 2040, the region of allowed flavor composition
at Earth will shrink ten-fold, and the flavor composition at the
astrophysical sources of the neutrinos will be inferred to within
6%, enough to pinpoint the dominant neutrino production mechanism
and to identify possible sub-dominant mechanisms. These conclusions
hold even in the nonstandard scenario where neutrino mixing is
non-unitary, a scenario that will be probed in next-generation
experiments such as the IceCube-Upgrade. As an illustration, we show
that future experiments are sensitive to decay rates of the heavier
neutrinos to below 1.8 × 10-5 (m/eV) s-1 at
95% credibility by 2040.