Table 1.

Full set of accuracy scores across all 27 dataset–algorithm combinations, shown in Fig. 3: root-mean-squared error (RMSE), mean absolute error (MAE), median absolute error (MDAE), Pearson’s correlation coefficient (PCC), and fluxomic features representation (FFR, the percentage of metabolic flux features over the total number of features)

Dataset(s)	Method	RMSE	MAE	MDAE	PCC	FFR, %
Single omics
GE	SVR	0.102 $\pm$ 3e-04*	0.067 $\pm$ 0.001*	0.045 $\pm$ 0.004	0.902 $\pm$ 0.001	0
GE	RF	0.127 $\pm$ 0.001	0.077 $\pm$ 4e-04	0.049 $\pm$ 0.001	0.864 $\pm$ 0.002	0
GE	ANN	0.122 $\pm$ 0.007	0.079 $\pm$ 0.008	0.053 $\pm$ 0.010	0.876 $\pm$ 0.004	0
MGE	SVR	0.115 $\pm$ 0.003	0.070 $\pm$ 4e-04	0.046 $\pm$ 2e-04	0.872 $\pm$ 0.006	0
MGE	RF	0.130 $\pm$ 0.001	0.079 $\pm$ 4e-04	0.050 $\pm$ 0.001	0.855 $\pm$ 0.002	0
MGE	ANN	0.139 $\pm$ 0.008	0.091 $\pm$ 0.008	0.065 $\pm$ 0.011	0.838 $\pm$ 0.005	0
MF	SVR	0.203 $\pm$ 0.006	0.117 $\pm$ 0.003	0.065 $\pm$ 3e-04	0.504 $\pm$ .033	100
MF	RF	0.185 $\pm$ 0.002	0.109 $\pm$ 0.001	0.065 $\pm$ 0.002	0.611 $\pm$ 0.009	100
MF	ANN	0.196 $\pm$ 0.009	0.125 $\pm$ 0.016	0.083 $\pm$ 0.021	0.588 $\pm$ 0.003	100
Early integration
GE-MF	SVR	0.132 $\pm$ 0.009	0.079 $\pm$ 0.004	0.048 $\pm$ 0.004	0.828 $\pm$ 0.029	36
GE-MF	RF	0.126 $\pm$ 0.001	0.077 $\pm$ 0.001	0.048 $\pm$ 0.001	0.866 $\pm$ 0.003	36
GE-MF	ANN	0.132 $\pm$ 0.007	0.085 $\pm$ 0.009	0.057 $\pm$ 0.011	0.847 $\pm$ 0.006	36
SGL data	SVR	0.117 $\pm$ 0.001	0.082 $\pm$ 3e-04	0.058 $\pm$ 0.001	0.867 $\pm$ 0.002	34
SGL data	RF	0.130 $\pm$ 0.001	0.082 $\pm$ 5e-04	0.053 $\pm$ 0.001	0.844 $\pm$ 0.003	34
SGL data	ANN	0.163 $\pm$ 0.011	0.105 $\pm$ 0.013	0.072 $\pm$ 0.019	0.805 $\pm$ 0.005	34
NSGA-II data	SVR	0.178 $\pm$ 0.014	0.103 $\pm$ 0.005	0.063 $\pm$ 0.002	0.653 $\pm$ 0.069	24
NSGA-II data	RF	0.179 $\pm$ 0.020	0.110 $\pm$ 0.010	0.067 $\pm$ 0.004	0.653 $\pm$ 0.077	24
NSGA-II data	ANN	0.154 $\pm$ 0.011	0.100 $\pm$ 0.014	0.067 $\pm$ 0.017	0.804 $\pm$ 0.013	24
iRF data	SVR	0.108 $\pm$ 0.002	0.072 $\pm$ 0.001	0.050 $\pm$ 0.001	0.891 $\pm$ 0.002	0
iRF data	RF	0.120 $\pm$ 0.001	0.074 $\pm$ 3e-04	0.049 $\pm$ 0.001	0.870 $\pm$ 0.002	0
iRF data	ANN	0.136 $\pm$ 0.008	0.090 $\pm$ 0.010	0.065 $\pm$ 0.014	0.854 $\pm$ 0.003	0
Intermediate and
late integration
GE and MF	BEMKL	0.182 $\pm$ 1e-04	0.110 $\pm$ 2e-04	0.066 $\pm$ 1e-04	0.626 $\pm$ 0.001	36
GE and MF	BRF	0.145 $\pm$ 0.001	0.086 $\pm$ 3e-04	0.053 $\pm$ 0.001	0.810 $\pm$ 0.003	36
GE and MF	MMANN	0.102 $\pm$ 0.001*	0.067 $\pm$ 0.001*	0.043 $\pm$ 0.002*	0.906 $\pm$ 0.002*	36
MGE and MF	BEMKL	0.182 $\pm$ 7e-05	0.110 $\pm$ 1e-04	0.067 $\pm$ 2e-04	0.625 $\pm$ 3e-04	79
MGE and MF	BRF	0.147 $\pm$ 0.001	0.087 $\pm$ 4e-04	0.054 $\pm$ 0.001	0.803 $\pm$ 0.003	79
MGE and MF	MMANN	0.112 $\pm$ 0.001	0.073 $\pm$ 0.001	0.047 $\pm$ 0.002	0.882 $\pm$ 0.003	79

Values in boldface type represent the best scores for each data integration scenario, while the best global performance for each measure is highlighted by an asterisk. The MMANN model consistently outperforms all other models and, with 36% of the features being fluxomic, demonstrates the utility of the additional metabolic modeling stage in our pipeline.