Accurate Thermophysical Properties of Water using Machine-Learned Potentials

TL;DR

The paper demonstrates that equivariant MACE machine-learned potentials can reproduce DFT-level thermophysical properties of RPBE-D3 water with high accuracy and enable statistically robust reweighting to the DFT ensemble. By comparing invariant and equivariant MACE models to kernel-based potentials, the authors show significantly lower total-energy and force errors for the L=2 equivariant network, which permits reliable reweighting and validation of ensemble averages. Key findings include a density maximum near 289 K, a melting point around 283.8 K, diffusion constants in good agreement with experiment, and overstructured RDFs likely due to neglected nuclear quantum effects. The work underscores the practical value of equivariant ML potentials for accurate, ensemble-validated predictions of water’s thermophysical properties and highlights considerations for training data and long-range interactions.

Abstract

Simulating water from first principles remains a significant computational challenge due to the slow dynamics of the underlying system. Although machine-learned interatomic potentials (MLPs) can accelerate these simulations, they often fail to achieve the required level of accuracy for reliable uncertainty quantification. In this study, we use MACE - an equivariant graph neural network architecture that has been trained using an extensive RPBE-D3 database - to predict density isobars, diffusion constants, radial distribution functions, and melting points. Although equivariant MACE models are computationally more expensive than simpler architectures, such as kernel-based potentials (KbPs), their significantly lower total energy errors allow for reliable thermodynamic reweighting with minimal bias. Our results are consistent with those of previous studies using KbPs; however, equivariant models can be validated against the ground-truth density functional theory (DFT) ensemble, providing a critical advantage. These findings establish equivariant MLPs as robust and reliable tools for investigating the thermophysical properties of water with DFT-level accuracy.

Figures (8)

• Figure 1: Density isobars of water for 128 molecule simulations obtained by parallel tempering for kbP and MACE. The data points for 1024 molecules were obtained without parallel tempering, but align within uncertainties with the 128 molecule results.
• Figure 2: Internal energies of the interface simulations during melting and freezing using MACE L=2 potentials.
• Figure 3: Diffusion constants obtained from the MACE L=2 potential. KbP results from montero_de_hijes_comparing_2024, Experimental data reproduced from gillen_selfdiffusion_1972holz_temperature-dependent_2000.
• Figure 4: Hydrogen-oxygen partial radial distribution function at different temperatures, calculated at the respective equilibrium volume with MACE L=2 potentials. The KbP results are from Ref. montero_de_hijes_comparing_2024.
• Figure 5: Oxygen-oxygen partial radial distribution function at different temperatures, calculated at the respective equilibrium volume with MACE L=2 potentials. The KbP results are from Ref. montero_de_hijes_comparing_2024.