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Simulations, Data Analysis and Algorithms

Table 7 Features selected by PCE. For each post-impact property, the PCE algorithm selects a subset of features to use in the model. For most post-impact parameters, the algorithm selects pre-impact parameters related to the impact geometry (γ, \(b_{\infty }\), \(v_{\infty }\)). Where other pre-impact properties have been selected, they tend to have a physically intuitive relationship to the post-impact property. Note that PCE did not select the pre-impact azimuthal orientations, \(\phi _{\mathrm{targ}}\) and \(\phi _{\mathrm{proj}}\), indicating that these properties generally do not play a role in determining collision outcomes

From: Machine learning applied to simulations of collisions between rotating, differentiated planets

Parameter Features selected
\(M_{\mathrm{LR}}\) \(M_{\mathrm{tot}}\), γ, \(b_{\infty }\), \(v_{\infty }\)
\(M^{\mathrm{norm}}_{\mathrm{LR}}\) γ, \(b_{\infty }\), \(v_{\infty }\)
\(F^{\mathrm{core}}_{\mathrm{LR}}\) γ, \(b_{\infty }\), \(v_{\infty }\), \(F^{\mathrm{core}}_{\mathrm{targ}}\), \(F^{\mathrm{core}}_{\mathrm{proj}}\)
\(J_{\mathrm{LR}}\) \(M_{\mathrm{tot}}\), γ, \(b_{\infty }\), \(v_{\infty }\), \(\Omega _{\mathrm{targ}}\), \(\theta _{\mathrm{targ}}\)
\(\Omega _{\mathrm{LR}}\) γ, \(b_{\infty }\), \(v_{\infty }\), \(\Omega _{\mathrm{targ}}\), \(\theta _{\mathrm{targ}}\), \(F^{\mathrm{core}}_{\mathrm{targ}}\)
\(\theta _{\mathrm{LR}}\) γ, \(b_{\infty }\), \(v_{\infty }\), \(\Omega _{\mathrm{targ}}\), \(\theta _{\mathrm{targ}}\)
\(F^{\mathrm{cond}}_{\mathrm{LR}}\) γ, \(b_{\infty }\), \(v_{\infty }\)
\(\delta ^{\mathrm{mix}}_{\mathrm{LR}}\) γ, \(b_{\infty }\), \(v_{\infty }\)
\(M_{\mathrm{SLR}}\) \(M_{\mathrm{tot}}\), γ, \(b_{\infty }\), \(v_{\infty }\)
\(M^{\mathrm{norm}}_{\mathrm{SLR}}\) γ, \(b_{\infty }\), \(v_{\infty }\)
\(F^{\mathrm{core}}_{\mathrm{SLR}}\) γ, \(b_{\infty }\), \(v_{\infty }\), \(F^{\mathrm{core}}_{\mathrm{targ}}\), \(F^{\mathrm{core}}_{\mathrm{proj}}\)
\(J_{\mathrm{SLR}}\) \(M_{\mathrm{tot}}\), γ, \(b_{\infty }\), \(v_{\infty }\)
\(\Omega _{\mathrm{SLR}}\) γ, \(b_{\infty }\), \(v_{\infty }\), \(\Omega _{\mathrm{proj}}\), \(F^{\mathrm{core}}_{\mathrm{proj}}\)
\(\theta _{\mathrm{SLR}}\) γ, \(b_{\infty }\), \(v_{\infty }\), \(\theta _{\mathrm{targ}}\), \(F^{\mathrm{core}}_{\mathrm{targ}}\), \(\Omega _{\mathrm{proj}}\), \(\theta _{\mathrm{proj}}\), \(F^{\mathrm{core}}_{\mathrm{proj}}\)
\(F^{\mathrm{cond}}_{\mathrm{SLR}}\) \(b_{\infty }\), \(v_{\infty }\), \(\Omega _{\mathrm{targ}}\), \(F^{\mathrm{core}}_{\mathrm{proj}}\)
\(\delta ^{\mathrm{mix}}_{\mathrm{SLR}}\) \(b_{\infty }\), \(v_{\infty }\)
\(M_{\mathrm{deb}}\) \(M_{\mathrm{tot}}\), \(b_{\infty }\), \(v_{\infty }\)
\(M^{\mathrm{norm}}_{\mathrm{deb}}\) \(b_{\infty }\), \(v_{\infty }\)
\(F^{\mathrm{Fe}}_{\mathrm{deb}}\) \(b_{\infty }\), \(v_{\infty }\), \(F^{\mathrm{core}}_{\mathrm{targ}}\), \(F^{\mathrm{core}}_{\mathrm{proj}}\)
\(\delta ^{\mathrm{mix}}_{\mathrm{deb}}\) γ, \(b_{\infty }\), \(v_{\infty }\), \(F^{\mathrm{core}}_{\mathrm{targ}}\), \(F^{\mathrm{core}}_{\mathrm{proj}}\)
\(\bar{\theta }_{\mathrm{deb}}\) γ, \(v_{\infty }\), \(\Omega _{\mathrm{targ}}\), \(\theta _{\mathrm{targ}}\), \(F^{\mathrm{core}}_{\mathrm{targ}}\), \(\theta _{\mathrm{proj}}\)
\(\theta ^{\mathrm{stdev}}_{\mathrm{deb}}\) \(M_{\mathrm{tot}}\), γ, \(b_{\infty }\), \(v_{\infty }\)
\(\bar{\phi }_{\mathrm{deb}}\) γ, \(b_{\infty }\), \(v_{\infty }\)
\(\phi ^{\mathrm{stdev}}_{\mathrm{deb}}\) γ, \(b_{\infty }\), \(v_{\infty }\), \(F^{\mathrm{core}}_{\mathrm{targ}}\), \(F^{\mathrm{core}}_{\mathrm{proj}}\)