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Page 8 of 18 Liu et al. J. Mater. Inf. 2025, 5, 27 I http://dx.doi.org/10.20517/jmi.2024.105

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Figure 2. Sketch-map visualization of the FT DP downstream dataset. Each point of this map represents an individual atomic configuration.
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The position of each point is determined by t-SNE of the learned descriptor of FT DP model, and its color indicates the corresponding
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formation energy of the structure. FT DP: Fine-tuned Fischer-Tropsch deep potential; t-SNE: t-distribution stochastic neighbor embedding
rate may be too large to be suitable for our fine-turning tasks owing to the loss of global knowledge in model
descriptor after over-fitting in downstream dataset and possible gradient explosion in training practices. As a
result, a relatively low initial learning rate 2 × 10 was utilized together with one million training batches in
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our fine-tuning protocol.

To evaluate the generalizability of the FT DP model, we performed a validation test where a model, named
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FT DP-80p, was trained on a randomly selected 80% subset and tested on the remaining 20%. Validation
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results [Supplementary Figure 1, Table 2] present parity plots of formation energies and atomic forces, along-
side R values, as well as the mean absolute error (MAE) and the root mean square error (RMSE) metrics
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comparing model predictions to DFT-calculated energies and forces. The FT DP-80p model achieved com-
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parable performance on training and validation subsets, confirming the robust generalizability. Furthermore,
the accuracy of the final FT DP model fine-tuned on the entire dataset is demonstrated in Figure 3A and B
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and Table 2 (final column), showing strong agreement between FT DP prediction and DFT calculation for
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energies and forces. Moreover, the violin plots in Figure 3C and D illustrate the distribution of energy differ-
ence and atomic force difference between FT DP prediction and DFT results, showing that although there are
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some outliers in a relatively wide range, our FT DP model still achieves a good accuracy with energy deviation
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of less than 3 meV/Atom and a force deviation of less than 0.09 eV/Å for 75% of the FT DP dataset. All these
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results indicate the model’s promising reliability for direct usage in high-efficiency structural optimization and
TS searching tasks. The accuracy of the final FT DP model will be further demonstrated below by comparing
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FT DP and DFT results for the lots of structures that emerged from atomistic modeling practices.
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Additionally, it is valuable to identify outlier structures with high prediction errors to investigate their charac-