Are galactic star formation and quenching governed by local, global or environmental phenomena?

We present an analysis of star formation and quenching in the SDSS-IV MaNGA-DR15, utilising over 5 million spaxels from $\sim$3500 local galaxies. We estimate star formation rate surface densities ($\Sigma_{\rm SFR}$) via dust corrected $H\alpha$ flux where possible, and via an empirical relationship between specific star formation rate (sSFR) and the strength of the 4000 Angstrom break (D4000) in all other cases. We train a multi-layered artificial neural network (ANN) and a random forest (RF) to classify spaxels into `star forming' and `quenched' categories given various individual (and groups of) parameters. We find that global parameters (pertaining to the galaxy as a whole) perform collectively the best at predicting when spaxels will be quenched, and are substantially superior to local/ spatially resolved and environmental parameters. Central velocity dispersion is the best single parameter for predicting quenching in central galaxies. We interpret this observational fact as a probable consequence of the total integrated energy from AGN feedback being traced by the mass of the black hole, which is well known to correlate strongly with central velocity dispersion. Additionally, we train both an ANN and RF to estimate $\Sigma_{\rm SFR}$ values directly via regression in star forming regions. Local/ spatially resolved parameters are collectively the most predictive at estimating $\Sigma_{\rm SFR}$ in these analyses, with stellar mass surface density at the spaxel location ($\Sigma_*$) being by far the best single parameter. Thus, quenching is fundamentally a global process but star formation is governed locally by processes within each spaxel.