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Extracting information from the total matter power spectrum with theprecision needed for upcoming cosmological surveys requires unraveling thecomplex effects of galaxy formation processes on the distribution of matter. Weinvestigate the impact of baryonic physics on matter clustering at $z=0$ usinga library of power spectra from the Cosmology and Astrophysics with MachinELearning Simulations (CAMELS) project, containing thousands of $(25\,h^{-1}{\rmMpc})^3$ volume realizations with varying cosmology, initial random field,stellar and AGN feedback strength and sub-grid model implementation methods. Weshow that baryonic physics affects matter clustering on scales $k \gtrsim0.4\,h\,\mathrm{Mpc}^{-1}$ and the magnitude of this effect is dependent on thedetails of the galaxy formation implementation and variations of cosmologicaland astrophysical parameters. Increasing AGN feedback strength decreases halobaryon fractions and yields stronger suppression of power relative to N-bodysimulations, while stronger stellar feedback often results in weaker effects bysuppressing black hole growth and therefore the impact of AGN feedback. We finda broad correlation between mean baryon fraction of massive halos ($M_{\rm200c} > 10^{13.5}$\,\Msun) and suppression of matter clustering but withsignificant scatter compared to previous work owing to wider exploration offeedback parameters and cosmic variance effects. We show that a random forestregressor trained on the baryon content and abundance of halos across the fullmass range $10^{10} \leq M_\mathrm{halo}/$\Msun$< 10^{15}$ can predict theeffect of galaxy formation on the matter power spectrum on scales $k =1.0$--20.0\,$h\,\mathrm{Mpc}^{-1}$.

Predicting the impact of feedback on matter clustering with machine learning in CAMELS