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Table 6 Coefficients of determination (\(\mathrm{r^{2}}\)-scores) for the analytic, semi-analytic, and data-driven methods investigated in this work. The data-driven models were trained on the train dataset and all models were evaluated on the holdout test dataset. The \(\mathrm{r^{2}}\)-scores quantify the correlation between the predicted and “true” values of the post-impact parameters, where the true values are obtained from SPH simulations. Entries listed as \(n/a\) indicate the method was not designed to make a prediction for the parameter in question. Mass and angular momentum properties reflect the performance of the classification step, whereas the other properties quantify only the regression performance (see: Sect. 3.6.3). The (semi-)analytic methods use the classification scheme inherent to those methods, while the data-driven methods use a multiclass XGB classifier

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

Parameter (Semi-)analytic Data-driven
PIM IEM EDACM PCE GP XGB MLP
ξ −1.1196 0.7518 0.6421 0.9733 0.9355 0.9793 0.9896
\(M_{\mathrm{LR}}\) −0.0392 0.7698 0.6932 0.9741 0.9571 0.9829 0.9863
\(M^{\mathrm{norm}}_{\mathrm{LR}}\) −1.7384 0.3950 0.2436 0.9415 0.9031 0.9747 0.9803
\(F^{\mathrm{core}}_{\mathrm{LR}}\) 0.5549 n/a −0.0792 0.9564 0.9450 0.9516 0.9568
\(J_{\mathrm{LR}}\) −144.4870 n/a n/a 0.8162 0.7857 0.9121 0.9045
\(\Omega _{\mathrm{LR}}\) −347.4151 n/a n/a 0.8831 0.8702 0.9229 0.9133
\(\theta _{\mathrm{LR}}\) −0.9391 n/a n/a 0.8589 0.8278 0.8852 0.8764
\(F^{\mathrm{melt}}_{\mathrm{LR}}\) n/a n/a n/a 0.9084 0.9647 0.9762 0.9798
\(\delta ^{\mathrm{mix}}_{\mathrm{LR}}\) −1.2559 n/a n/a 0.9251 0.8942 0.9710 0.9747
\(M_{\mathrm{SLR}}\) −1.7159 −1.7159 0.0773 0.9601 0.8257 0.9442 0.9418
\(M^{\mathrm{norm}}_{\mathrm{SLR}}\) −4.2472 −4.2472 −1.3057 0.9409 0.7052 0.9317 0.9028
\(F^{\mathrm{core}}_{\mathrm{SLR}}\) n/a n/a n/a 0.9141 0.9265 0.9426 0.9332
\(J_{\mathrm{SLR}}\) n/a n/a n/a 0.8893 0.8285 0.8819 0.8713
\(\Omega _{\mathrm{SLR}}\) n/a n/a n/a 0.8803 0.9140 0.9044 0.9073
\(\theta _{\mathrm{SLR}}\) n/a n/a n/a 0.8080 0.7933 0.8176 0.7969
\(F^{\mathrm{melt}}_{\mathrm{SLR}}\) n/a n/a n/a 0.9272 0.9720 0.9693 0.9749
\(\delta ^{\mathrm{mix}}_{\mathrm{SLR}}\) n/a n/a n/a 0.7864 0.7897 0.8171 0.7714
\(M_{\mathrm{deb}}\) −0.5495 0.8635 0.7346 0.9672 0.9647 0.9867 0.9933
\(M^{\mathrm{norm}}_{\mathrm{deb}}\) −0.8056 0.8448 0.7469 0.9848 0.9685 0.9895 0.9937
\(F^{\mathrm{Fe}}_{\mathrm{deb}}\) n/a n/a n/a 0.9419 0.8811 0.9396 0.9538
\(\delta ^{\mathrm{mix}}_{\mathrm{deb}}\) n/a n/a n/a 0.6436 0.5257 0.6747 0.6722
\(\bar{\theta }_{\mathrm{deb}}\) n/a n/a −0.0227 0.3903 0.3364 0.4834 0.4653
\(\theta ^{\mathrm{stdev}}_{\mathrm{deb}}\) n/a n/a −12.0333 0.8680 0.8634 0.9095 0.8812
\(\bar{\phi }_{\mathrm{deb}}\) n/a n/a −19.7818 0.8168 0.7969 0.8603 0.8299
\(\phi ^{\mathrm{stdev}}_{\mathrm{deb}}\) n/a n/a −0.7637 0.7657 0.7475 0.8149 0.7787
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