Predictive power of polynomial machine learning potentials for liquid states in 22 elemental systems

TL;DR

The paper addresses predicting liquid-state structural properties across 22 elemental systems using a new polynomial rotational-invariant potential. It develops polynomial MLPs trained solely on solid-state DFT data and evaluates their predictions for liquids against DFT and traditional interatomic potentials. Across RDF, BADF, CN, and BOOP metrics, the polynomial MLPs achieve accuracy comparable to DFT, including in anomalous melting elements, and often outperform empirical potentials. This work demonstrates transferable, efficient liquid-state modeling and highlights limitations of simpler potentials for complex liquid environments.

Abstract

The polynomial machine learning potentials (MLPs) described by polynomial rotational invariants have been systematically developed for various systems and used in diverse applications in crystalline states. In this study, we systematically investigate the predictive power of the polynomial MLPs for liquid structural properties in 22 elemental systems with diverse chemical bonding properties, including those showing anomalous melting behavior, such as Si, Ge, and Bi. We compare liquid structural properties obtained from molecular dynamics simulations using the density functional theory (DFT) calculation, the polynomial MLPs, and other interatomic potentials in the literature. The current results demonstrate that the polynomial MLPs consistently exhibit high predictive power for liquid structural properties with the same accuracy as that of typical DFT calculations.

Figures (35)

• Figure 1: Distribution of the energies of structures in the training and test datasets computed using the DFT calculation and those calculated using the polynomial MLP, which has the lowest prediction error. The vertical axis range is fixed to 1.4 eV/atom, although structures with energy values higher than the energy range are included in the datasets. The numerical values enclosed in the squares represent the root square mean errors (RMSEs) for the energy, which are estimated using the test datasets.
• Figure 2: Absolute prediction errors of the cohesive energy for 86 prototype structures in elemental Li, Si, Ga, Ge, Cd, In, Hg, and Bi. The absolute prediction errors for the other systems can be found in the supplemental material.
• Figure 3: (a) Mean RDF errors of the polynomial MLPs in Si and Ge. The mean RDF error was calculated by averaging the RDF errors at the six temperatures. The computational time on the horizontal axis is regarded as the model complexity of the polynomial MLP. (b) RDFs and BADFs computed using the three polynomial MLPs, (1), (2), and (3), highlighted in (a) at 1750 and 1300 K in Si and Ge, respectively. The RDFs and BADFs at each polynomial MLP are shifted upwards by the amounts of 1.0 and 0.01, respectively. The black solid and orange dotted lines indicate the distribution functions computed using the DFT calculation and the polynomial MLP, respectively.
• Figure 4: RDFs, BADFs, running CNs, and BOOPs obtained from MD simulations using the polynomial MLPs in elemental Si and Ge. The polynomial MLP showing the lowest mean RDF error is employed for each system. The structural quantities calculated using the DFT calculation, the Tersoff potentials Si_tersoffGe_tersoff, the MEAM potentials Si_MEAMGe_MEAM, and the quadratic SNAPs SNAP are also shown for comparison. The RDFs and BADFs at each temperature are shifted upwards by the amounts of 1.0 and 0.01, respectively. The running CNs and BOOPs were calculated at 1750 and 1300 K in Si and Ge, respectively, which are close to their melting temperatures. The black solid and orange dotted lines indicate the structural quantities computed using the DFT calculation and the polynomial MLP, respectively. In the legend, Poly. MLP and Quad. SNAP stand for polynomial MLP and quadratic SNAP, respectively.
• Figure 5: Structural quantities obtained from MD simulations using the polynomial MLP in elemental Li. The polynomial MLP showing the lowest mean RDF error was employed. The structural quantities calculated using the DFT calculation, the MEAM potential Li_MEAM, and the quadratic SNAP SNAP are also shown for comparison. The RDFs and BADFs shown in the top-left and top-right panels, respectively, were obtained at three temperatures above the melting temperature. The RDFs and BADFs at each temperature are shifted upwards by the amounts of 1.0 and 0.01, respectively. The running CNs and BOOPs shown in the bottom-left and bottom-right panels, respectively, were calculated at the lowest temperature among the three temperatures, which was closest to the melting temperature. The black solid and orange dotted lines indicate the structural quantities computed using the DFT calculation and the polynomial MLP, respectively. In the legend, Poly. MLP and Quad. SNAP stand for polynomial MLP and quadratic SNAP, respectively.