  In this work, we investigate the nature of the strong coupling constant and
related physics. Through the analysis of accumulated experimental data from
around the world, we employ the ability of machine learning to unravel its
physical laws. The result of our efforts is a formula that captures the
expansive panorama of the distribution of the strong coupling constant across
the entire energy range. Importantly, this newly derived expression is very
similar to the formula derived from the Dyson-Schwinger equations based on the
framework of Yang-Mills theory. By introducing the Euler number, $e$, into the
functional formula of the strong coupling constant at high energies, we have
successfully solved the puzzle of the infrared divergence, which allows for a
seamless transition of the strong coupling constant from the perturbative to
the non-perturbative energy regime. Moreover, the obtained ghost and gluon
dressing function distribution results confirm that the obtained strong
coupling constant formula can well describe the physical properties of the
non-perturbed regime. In addition, we investigate the QCD strong coupling
constant result of the Bjorken sum rule $\Gamma_1^{p-n}$ and the quark-quark
static energy $E_0(r)$, and find that the global energy scale can effectively
interpret the experimental data. The results presented in this work shed light
on the puzzling properties of quantum chromodynamics and the intricate
interplay of strong coupling constants at both low and high energy scales.
