Abstract
When training deep neural networks using first-principles calculation data to obtain potential functions for molecular dynamics simulations, extensive model capability evaluation work is required. However, the commonly used validation sets for model evaluation are limited by the high cost of obtaining first-principles data, making it difficult to comprehensively assess the strong generalization ability of deep neural network trained models, which requires coverage of a much larger space than the training set samples. This manuscript proposes a short bond evaluation method and conducts evaluation experiments using this method and the self-consistent field labeling evaluation method on multiple tasks under different structures generalization in two complex reaction systems. It also performs correlation analysis between the results of the two methods to validate and explain the applicability and effectiveness of the proposed method. Although this method has the necessary and insufficient characteristics, the results show that this method can accelerate the assessment of model generalization capabilities while maintaining the reliability of the evaluation results. Moreover, this method can particularly accelerate the high-accuracy filter of poor-performing models, thereby helping to improve the convergence speed during the model training iteration process. At the same time, it achieves a significant reduction in evaluation costs.
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The data that support the results of this study are available from the corresponding author upon reasonable request.
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The code for computational analysis is available from the corresponding author upon reasonable request.
References
Wang, H., Zhang, L. & Han, J. DeePMD-kit: A deep learning package for many-body potential energy representation and molecular dynamics. Comput. Phys. Commun. 228, 178–184 (2018).
Liang, W., Zeng, J., York, D. M., Zhang, L. & Wang, H. Learning deepmd-kit: A guide to building deep potential models. A practical guide to recent advances in multiscale modeling and simulation of biomolecules, 1–20 (2023).
Zeng, J. et al. DeePMD-kit v2: A software package for deep potential models. J. Chem. Phys. 159 (2023).
Prašnikar, E., Ljubič, M., Perdih, A. & Borišek, J. Machine learning heralding a new development phase in molecular dynamics simulations. Artif. Intell. Rev. 57, 102 (2024).
Xie, K. et al. Neural network potential for Zr–Rh system by machine learning. J. Phys.: Condens. Matter. 34, 075402 (2021).
You, Y. et al. Principal component analysis enables the design of deep learning potential precisely capturing LLZO phase transitions. npj Comput. Mater. 10, 57 (2024).
Wang, J. et al. A deep learning interatomic potential developed for atomistic simulation of carbon materials. Carbon. 186, 1–8 (2022).
Ganser, R. et al. Mechanism of antiferroelectricity in polycrystalline ZrO2. Adv. Funct. Mater. 34, 2405513 (2024).
Ding, C. J. et al. A deep learning interatomic potential suitable for simulating radiation damage in bulk tungsten. Tungsten. 6, 304–322 (2024).
Floryan, D. On instabilities in neural network-based physics simulators. arXiv:2406.13101 (2024).
Ardakani, M. H. & Aliavazi, M. Nickel (II) unsymmetrical Schiff base complex immobilized into three dimensional mesoporous silica KIT-6: a novel and efficient catalyst for selective oxidation of sulfides to sulfoxides. J. Porous Mater. 31, 473–482 (2024).
Kim, J. H. et al. Highly reliable and large-scale simulations of promising argyrodite solid-state electrolytes using a machine-learned moment tensor potential. Nano Energy. 124, 109436 (2024).
Yang M. et al. Ab Initio Accuracy Neural Network Potential for Drug-Like Molecules. Research 8, 0837 (2025).
Ragone, M., Shahabazian-Yassar, R., Mashayek, F. & Yurkiv, V. Deep learning modeling in microscopy imaging: A review of materials science applications. Prog. Mater Sci. 138, 101165 (2023).
Hosseini, S. & Pourmirzaee, R. Green policy for managing blasting induced dust dispersion in open-pit mines using probability-based deep learning algorithm. Expert Syst. Appl. 240, 122469 (2024).
Madhavan Namboothiri, K. et al. State of charge estimation of lithium-ion batteries employing deep neural network with variable learning rate. J. Inst. Eng. India Ser. B. 104, 277–284 (2023).
Ro, Y. et al. Dataset Efficient Training with Model Ensembling. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 4700–4704 (2023).
Pretnar Žagar, A. & Demšar, J. Model Evaluation. In Tourism on the Verge (253–274). Cham: Springer International Publishing (2022).
De-Chuan, Z. H. A. N., Xinchun, L. I., Shaoming, S. O. N. G. & Bingshuai, L. I. U. S. Model training method, data processing method, and apparatus. Patent Application No. 18/327, 952 (2023).
Ton, K. T., Aloise, D. & Contardo, C. On removing diverse data for training machine learning models. In Mathematical Analysis, Differential Equations and Applications, 761–783 (2024).
Hu, Q. et al. Test Optimization in DNN Testing: A Survey. ACM Transactions on Software Engineering and Methodology 33, 1–42 (2024).
Tamang, L. et al. Handling out-of-distribution data: a survey. In IEEE Transactions on Knowledge and Data Engineering, Vol. 37, 5948–5966 (IEEE, 2025).
Yang, J. et al. Generalized out-of-distribution detection: a survey. Int J Comput Vis. 132, 5635–5662 (2024).
Mohseni, S. et al. Self-supervised learning for generalizable out-of-distribution detection. In Proc. AAAI Conference on Artificial Intelligence, Vol. 34, 5216–5223 (2020).
Li, L. et al. Kohn-Sham equations as regularizer: building prior knowledge into machine-learned physics. Phys. Rev. Lett. 126, 036401 (2021).
Ye, X. et al. Molecular substructure graph attention network for molecular property identification in drug discovery. Pattern Recognit. 128, 108659 (2022).
Ishida, S., Miyazaki, T., Sugaya, Y. & Omachi, S. Graph neural networks with multiple feature extraction paths for chemical property estimation. Mol. 26, 3125 (2021).
Huang, M., Yu, H. & Zhang, J. A practical generalization metric for deep networks benchmarking. Sci. Rep. 15, 9747 (2025).
Ao, D., Hu, Z. & Mahadevan, S. Dynamics model validation using time-domain metrics. J. Verif. Valid. Uncert. 2, 011004 (2017).
Garrido, J. M. Object oriented simulation (Springer US, 2009).
Roach, L., Rignanese, G. M., Erriguible, A. & Aymonier, C. Applications of machine learning in supercritical fluids research. J. Supercrit. Fluids. 202, 106051 (2023).
Takase, T., Oyama, S. & Kurihara, M. Evaluation of stratified validation in neural network training with imbalanced data. In 2019 IEEE International Conference on Big Data and Smart Computing (BigComp), 1–4 (IEEE, 2019).
Xu, Y. & Goodacre, R. On splitting training and validation set: a comparative study of cross-validation, bootstrap and systematic sampling for estimating the generalization performance of supervised learning. J. Anal. Test. 2, 249–262 (2018).
Zhang, L. et al. Deep potential molecular dynamics: a scalable model with the accuracy of quantum mechanics. Phys. Rev. Lett. 120, 143001 (2018).
Cui, T. et al. Geometry-enhanced pretraining on interatomic potentials. Nat. Mach. Intell. 6, 428–436 (2024).
Lenhard, J., Stephan, S. & Hasse, H. On the History of the Lennard-Jones Potential. Ann. Phys. 536, 2400115 (2024).
Wang, X., Ramírez-Hinestrosa, S., Dobnikar, J. & Frenkel, D. The Lennard-Jones potential: when (not) to use it. Phys. Chem. Chem. Phys. 22, 10624–10633 (2020).
Malhotra, R. & Sharma, A. Threshold benchmarking for feature ranking techniques. Bull. Electr. Eng. Inform. 10, 1063–1070 (2021).
Chai, T. & Draxler, R. R. Root mean square error (RMSE) or mean absolute error (MAE). Geosci. Model Dev. Discuss. 7, 1525–1534 (2014).
Thompson, A. P. et al. LAMMPS-a flexible simulation tool for particle-based materials modeling at the atomic, meso, and continuum scales. Comput. Phys. Commun. 271, 108171 (2022).
Zhou, K. & Liu, B. Control techniques of molecular dynamics simulation. In Molecular Dynamics Simulation (Elsevier, 2022).
Asuero, A. G., Sayago, A. & González, A. G. The correlation coefficient: An overview. Crit. Rev. Anal. Chem. 36, 41–59 (2006).
Kresse, G. & Furthmüller, J. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comput. Mater. Sci. 6, 15–50 (1996).
Cickovski, T., Chatterjee, S., Wenger, J., Sweet, C. R. & Izaguirre, J. A. MDLab: A molecular dynamics simulation prototyping environment. J. Comput. Chem. 31, 1345–1356 (2010).
Mo, P. et al. High-speed and low-power molecular dynamics processing unit (MDPU) with ab initio accuracy. npj Comput. Mater. 10, 253 (2024).
Beatrice, A. C. Advancements and Future Directions in Molecular Dynamics (MD) Simulations. IDOSR J. Appl. Sci. 9, 21–26 (2024).
Goddard III, W. A. & Strachan, A. Atomistic-scale simulations of energetic materials with ReaxFF reactive force fields. In APS Shock Compression of Condensed Matter Meeting Abstracts, E5-001 (2005).
Michalak, A., Ziegler, T. Modeling Chemical Reactions with First-Principle Molecular Dynamics. Molecular Materials with Specific Interactions–Modeling and Design. 225–274Springer Netherlands: Dordrecht, (2007).
Massobrio, C. et al. Making computer materials real: The predictive power of first-principles molecular dynamics. In Theory and Simulation in Physics for Materials Applications: Cutting-Edge Techniques in Theoretical and Computational Materials Science (pp. 3–21). Cham: Springer International Publishing (2020).
Saxe P. et al. SEAMM: A Simulation Environment for Atomistic and Molecular Modeling. J. Phys. Chem. A. 129, 6973–6993 (2025).
Bohrium. Bohrium Quantum Computing Platform. Retrieved from https://bohrium.dp.tech (2024).
Blöchl, P. E. Projector augmented-wave method. Phys. Rev. B. 50, 17953 (1994).
Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865 (1996).
NOSÉ, S. U. I. A molecular dynamics method for simulations in the canonical ensemble. Mol. Phys. 100, 191–198 (2002).
Sun, J., Ruzsinszky, A. & Perdew, J. P. Strongly constrained and appropriately normed semilocal density functional. Phys. Rev. Lett. 115, 036402 (2015).
Ali, A. & Gravino, C. An empirical comparison of validation methods for software prediction models. J. Software: Evol. Process. 33, e2367 (2021).
Acknowledgements
This work was supported by the Major Science and Technology Projects in Yunnan Province (Grant No. 202302AB080009).
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X.C. conducted the calculations, generated and analyzed the data, interpreted the results, and prepared the first draft; Y.C. co-generated and analyzed the data, co-prepared the first draft; X.C. and Y.C. designed the workflow of the project and developed the Python code for GNN model; X.C. performed the DFT, FPMD and DPMD calculations and trained the DP models. Y.C. performed the trained the DP models. J.Z. co- assisted with data analysis and interpretation; All authors contributed to the final version of the manuscript.
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Chen, X., Chen, Y. & Zhou, J. Short bond evaluation method for rapidly assessing the generalization ability of deep neural network potential function models and its effectiveness verification. npj Comput Mater (2026). https://doi.org/10.1038/s41524-026-01957-7
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DOI: https://doi.org/10.1038/s41524-026-01957-7
