Machine-learned interatomic potentials (MLIP) trained to Density Functional Theory (DFT) enable linear scaling with the number of atoms at an accuracy on a par with DFT to predict macroscopic material properties, e.g. phase diagrams. However, the relationship between the obtained potential’s accuracy and the accuracy of the predicted physical property (e.g., bulk modulus, phase diagram…etc.) is non-trivial. It had been shown in DFT that both the systematic (i.e., the choice of the energy-cutoff and k-points mesh) and statistical error (the coupling of both) contribute to the uncertainty prediction of derived physical properties, e.g., bulk modulus [1]. In the same way MLIPs with a high degree of flexibility benefit the most from high precision DFT datasets [2], as otherwise the systematic error of the potential dominates the uncertainty in the DFT potential energy surface. In order to understand the effect of MLIPs on the uncertainty propagation to physical properties prediction, we developed a data-driven pyiron [3] workflows for fitting MLIPs and predicting physical properties. We demonstrate this by fitting the equation of state (EOS) and obtaining the bulk modulus of the material.

In this poster, we present a data-driven pyiron workflow applied to copper (Cu). Starting with the generation of a diverse training set using the Automated Small SYmmetric Structure Training (ASSYST) method [4]. Using this dataset, we train atomic cluster expansion (ACE) potentials [5] and highlight the key challenges in fitting MLIPs, including balancing accuracy and computational cost, as well as avoiding overfitting. The potentials are parameterized using the ladder step method based on a minimal basis set to achieve a given accuracy measured by root-mean-square error (RMSE) across both training and testing datasets. Finally, the potentials are applied to fit the EOS and quantify the uncertainty of the bulk modulus, pressure derivative of the bulk modulus, and equilibrium lattice constant. Using the developed workflow, this study can be extended to cover other physical properties.

References

[1] J. Janssen, et al. npj Comp. Mat. (2024) 10.1, 263

[2] I. Baghishov, et al. arXiv:2506.05646 (2025)

[3] J. Janssen, et al.  Comp. Mat. Sci. (2019) 163

[4] M. Poul, et al. npj Comp. Mat. Sci. (2025) 11.1: 1-15

[5] R. Drautz, Phys. Rev. B (2019) 99