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Achieving Empirical Potential Efficiency with DFT Accuracy: A Neuroevolution Potential for the $α$-Fe--C--H System

Fan-Shun Meng, Shuhei Shinzato, Zhiqiang Zhao, Jun-Ping Du, Lei Gao, Zheyong Fan, Shigenobu Ogata

TL;DR

The paper introduces a Neuroevolution Potential (NEP) for the ternary α-Fe–C–H system trained on spin-polarized DFT data, achieving DFT-level accuracy with empirical-potential efficiency. Through radial and angular atomic-environment descriptors within a Behler–Parrinello-like framework, NEP supports large-scale, GPU-accelerated MD with a single hidden-layer neural network, trained via separable natural evolution strategy. Efficiency benchmarks show NEP on CPUs is faster than NNIP and, on GPUs, enables multi-million-atom simulations with substantial speedups over traditional methods, while maintaining close agreement with DFT in energies and forces (RMSE$(E)\approx5.1$ meV/atom, RMSE$(F)\approx96$ meV/Å). Comprehensive accuracy tests across lattice properties, screw dislocations, and H behavior at Fe$_3$C and ferrite/cementite interfaces demonstrate NEP’s superior fidelity to DFT/NNIP compared with BOP, making it a practical tool for investigating hydrogen embrittlement in steel at large scales.

Abstract

A neuroevolution potential (NEP) for the ternary $α$-Fe--C--H system was developed based on a database generated from spin-polarized density functional theory (DFT) calculations, achieving empirical potential efficiency with DFT accuracy. At the same power consumption, simulation speeds using NEP are comparable to, or even faster than, those with bond order potentials. The NEP achieves DFT-level accuracy across a wide range of scenarios commonly encountered in studies of $α$-Fe- and $α$-Fe--C under hydrogen environments. The NEP enables large-scale atomistic simulations with DFT-level accuracy at the cost of empirical potentials, offering a practical tool to study hydrogen embrittlement in steel.

Achieving Empirical Potential Efficiency with DFT Accuracy: A Neuroevolution Potential for the $α$-Fe--C--H System

TL;DR

The paper introduces a Neuroevolution Potential (NEP) for the ternary α-Fe–C–H system trained on spin-polarized DFT data, achieving DFT-level accuracy with empirical-potential efficiency. Through radial and angular atomic-environment descriptors within a Behler–Parrinello-like framework, NEP supports large-scale, GPU-accelerated MD with a single hidden-layer neural network, trained via separable natural evolution strategy. Efficiency benchmarks show NEP on CPUs is faster than NNIP and, on GPUs, enables multi-million-atom simulations with substantial speedups over traditional methods, while maintaining close agreement with DFT in energies and forces (RMSE meV/atom, RMSE meV/Å). Comprehensive accuracy tests across lattice properties, screw dislocations, and H behavior at FeC and ferrite/cementite interfaces demonstrate NEP’s superior fidelity to DFT/NNIP compared with BOP, making it a practical tool for investigating hydrogen embrittlement in steel at large scales.

Abstract

A neuroevolution potential (NEP) for the ternary -Fe--C--H system was developed based on a database generated from spin-polarized density functional theory (DFT) calculations, achieving empirical potential efficiency with DFT accuracy. At the same power consumption, simulation speeds using NEP are comparable to, or even faster than, those with bond order potentials. The NEP achieves DFT-level accuracy across a wide range of scenarios commonly encountered in studies of -Fe- and -Fe--C under hydrogen environments. The NEP enables large-scale atomistic simulations with DFT-level accuracy at the cost of empirical potentials, offering a practical tool to study hydrogen embrittlement in steel.
Paper Structure (9 sections, 7 equations, 7 figures, 2 tables)

This paper contains 9 sections, 7 equations, 7 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Methodology
  3. Efficiency of the NEP for the $\alpha$-Fe--C--H system
  4. Accuracy of the NEP for the $\alpha$-Fe--C--H system
  5. Overall accuracy of the $\mathrm{NEP}$
  6. The NEP performance for the fundamental properties of $\alpha$-Fe-C-H
  7. The NEP performance for C/H in screw dislocation
  8. The NEP performance for H in cementite and ferrite-cementite interface
  9. Conclusion

Figures (7)

  • Figure 1: Visualization of the database in the descriptor space using the Principal Component Analysis. PC indicates the principal component.
  • Figure 2: Computational cost of NEP compared with that of NNIP and BOP using LAMMPS on CPU and using GPUMD on GPU platforms. NEP${\_}$ H/A100-scaled indicates that the computational costs were normalized with respect to the power consumption (in watts) of the CPU and GPU employed in this test, see the main text.
  • Figure 3: Comparison of NEP and DFT (a) energies and (b) forces of the structures in the training and testing data sets. The dotted line with a slope of 1 corresponds to a perfect training.
  • Figure 4: Point defects in Fe$_3$C (a) and the corresponding formation energies (b). C-vac, C-int, Fe$_1$-anti-C in (a) stand for C vacancy, interstitial atom of C, and Fe$_1$ atom replaced by a C atom, same rule can be applied to other cases. The defect formation energy from BOPzhou2020review, NNIPmeng2025high and DFTjiang2008point were also plotted in (b).
  • Figure 5: Configurations of C-decorated kinks and their migration energy barriers. (a)-(b) local atomic configuration of Kinks with C-C separation of 1b and 2b in the Burgers vector direction. $\text{K}^+$ and $\text{K}^-$ stand for the nonequivalent kinks. Gray and red balls stand for Fe and C atoms, respectively. (c) Energy barriers for the 4 types of C-decorated kinks, compared with results from NNIPmeng2025high and DFTventelon2023mobility.
  • ...and 2 more figures