  Stellar feedback-driven outflows regulate the stellar formation and chemical
enrichment of galaxies, yet the underlying dependence of mass outflow rate on
galaxy properties remains largely unknown. We develop a simple yet
comprehensive non-equilibrium chemical evolution model~(NE-CEM) to constrain
the mass-loading factor $\eta$ of outflows using the metallicity-stellar
mass-SFR relation observed by SDSS at $z{=}0$. Our NE-CEM predicts the chemical
enrichment by explicitly tracking both the histories of star formation and
mass-loading. After exploring the EAGLE simulation, we discover a compact yet
flexible model that accurately describes the average star formation histories
of galaxies. Applying a novel method of chemically measuring $\eta$ to EAGLE,
we find $\eta$ can be parametrised by its dependence on stellar mass and
specific SFR as $\log\eta\propto M_*^{\alpha}s{\mathrm{SFR}}^{\beta}$, with
$\alpha{=}{-}0.12$ and $\beta{=}0.32$ in EAGLE. Our chemically-inferred $\eta$
agrees remarkably well with the kinematic measurements by Mitchell et al. After
extensive tests with EAGLE, we apply an NE-CEM Bayesian analysis to the SDSS
data, yielding a tight constraint of
$\log(\eta/0.631)=0.731{\pm}0.002\times(M_*/10^{9.5}M_{\odot})^{-0.222\pm0.004}
(s{\mathrm{SFR}}/10^{-9.5}yr^{-1})^{0.078\pm0.003}$, in good agreement with the
down-the-barrel measurements. Our best-fitting NE-CEM not only accurately
describes the metallicity-stellar mass-SFR relation at $z{=}0$, but also
successfully reproduce the so-called "fundamental metallicity relation'' at
higher redshifts. Our results reveal that different galaxies form stars and
enrich their gas in a non-equilibrium but strikingly coherent fashion across
cosmic time.
