  Mass is a fundamental property and an important fingerprint of atomic
nucleus. It provides an extremely useful test ground for nuclear models and is
crucial to understand energy generation in stars as well as the heavy elements
synthesized in stellar explosions. Nuclear physicists have been attempting at
developing a precise, reliable, and predictive nuclear model that is suitable
for the whole nuclear chart, while this still remains a great challenge even in
recent days. Here we employ the Fourier spectral analysis to examine the
deviations of nuclear mass predictions to the experimental data and to present
a novel way for accurate nuclear mass predictions. In this analysis, we map the
mass deviations from the space of nucleon number to its conjugate space of
frequency, and are able to pin down the main contributions to the model
deficiencies. By using the radial basis function approach we can further
isolate and quantify the sources. Taking a pedagogical mass model as an
example, we examine explicitly the correlation between nuclear effective
interactions and the distributions of mass deviations in the frequency domain.
The method presented in this work, therefore, opens up a new way for improving
the nuclear mass predictions towards a hundred kilo-electron-volt accuracy,
which is argued to be the chaos-related limit for the nuclear mass predictions.
