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Liu et al. J. Mater. Inf. 2025, 5, 27 I http://dx.doi.org/10.20517/jmi.2024.105 Page 9 of 18

Table 2. Validation results of the FT DP models
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FT DP-80p on FT DP-80p on Final FT DP on
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Test items
the training set the validation set the entire dataset
Number of structures 24,525 6,131 30,656
Energy parity plot R 2 1.000 1.000 1.000
Energy MAE (eV) 0.1837 0.1890 0.1829
Energy RMSE (eV) 0.3141 0.3233 0.3112
Energy MAE
(meV/atom) 5.497 5.780 5.500
Energy RMSE
(meV/atom) 10.02 10.85 9.974
Force parity plot R 2 0.9605 0.9480 0.9570
Force MAE (eV/Å) 0.0764 0.0792 0.0764
Force RMSE (eV/Å) 0.1167 0.1271 0.1167

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FT DP: Fine-tuned Fischer-Tropsch deep potential; MAE: mean absolute error; RMSE: root
mean square error.

teristics and similarities. Structures in the entire FT DP dataset with the top ten highest absolute prediction
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errors in energies (|Δ |) and maximum absolute prediction errors in atomic forces (|Δ | ) are presented in
Supplementary Tables 1 and 2 and Supplementary Figures 2 and 3, respectively. We observe that most of these
structures exhibit disordered configurations or unphysical features. For example, 60% of these structures cor-
respondtothe samechemicalformula C 6H 12O 6, displayingdisordered molecularconfigurationsin a relatively
small cubic cell with lattice vector equals to 10Å, rendering their physical state (gas/liquid/solid) indetermi-
nate. Moreover, the third- and sixth-ranked structures in |Δ | contain unphysical H 6 clusters located in the
vacuum layer of Fe 16H 7 surfaces. While these outliers reflect the equilibrium diversity of the dataset, which
could improve model stability in the non-equilibrium region [70] , they also highlight the presence of unphysi-
cal configurations that necessitate data cleaning to remove the outliers for preventing training instability and
downgraded model performance in practical atomistic modeling applications.

Reaction pathways
Many previous studies have demonstrated that certain surfaces exhibit much higher FTS activity, identifying
them as the active surfaces [6,71] . A well-known example is the -Fe 5C 2(510) surface, which has been shown
to present relatively low CO dissociation and C-C coupling barriers [16,24,25] . In this section, the FT DP model
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and our D2S TS optimization workflow are utilized to investigate the key elementary reactions of FTS reaction
pathways on the A-P5 site of -Fe 5C 2 (510) surface, known as an important active site for FTS process due
to the participation of the lattice carbon and carbon vacancy on it in the surface reaction through a Mars-von
Krevelen (MvK) mechanism revealed by previous studies [6,24,25] . In particular, we consider the dissociative
adsorption of H 2 by Langmuir-Hinshelwood (L-H) mechanism, the dissociative adsorption of CO by the MvK
mechanism, the competition between chaingrowth (C-C coupling) and carbon hydrogenation (C-H coupling)
for carbon adsorbates, and the desorption of hydrocarbon compounds such as CH 4. The MvK reaction mech-
anism similar to previous works is also revealed in our investigation, especially for CO dissociation and chain
growth process, illustrating the importance of the A-P5 site on iron carbide for FTS.

To further validate the accuracy of the FT DP model in the TS optimization, we compared the results from
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three types of calculations: (1) purely FT DP-based; (2) DFT single-point calculation after TS optimization
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by FT DP, denoted as DFT@FT DP; and (3) purely DFT-based, in Figure 4, illustrating that most reaction
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2