Automated Prediction of Thermodynamic Properties via Bayesian Free-Energy Reconstruction from Molecular Dynamics

TL;DR

The work tackles accurate thermodynamic predictions by uniting MD with Bayesian free-energy reconstruction. It advances a workflow that reconstructs the Helmholtz free-energy surface $F(V,T)$ from irregular MD data using Gaussian Process Regression, while incorporating quantum effects via zero-point energy corrections from harmonic/quasi-harmonic theory and propagating uncertainties through the model. An active-learning strategy optimizes sampling in the volume–temperature space, enabling efficient, automated thermodynamics for both crystalline and liquid phases. Applied to nine elemental metals with 20 interatomic potentials, the method yields thermodynamic properties and melting behavior with quantified confidence, providing a robust benchmark for interatomic potentials and a path toward high-throughput thermodynamics. Overall, the framework offers a general, uncertainty-aware tool that integrates MD, quantum corrections, and Bayesian inference to enable automated, transferable thermodynamics across materials and phases.

Abstract

Accurate free-energy calculations are essential for predicting thermodynamic properties and phase stability, but existing methods are limited: phonon-based approaches neglect anharmonicity and liquids, while molecular dynamics (MD) is computationally demanding, neglects low-temperature quantum effects, and often requires manual planning and post-processing of simulations. We present a unified workflow that reconstructs the Helmholtz free-energy surface from MD data using Gaussian Process Regression (GPR), augmented with zero-point energy corrections from harmonic/quasi-harmonic theory. The framework propagates statistical uncertainties, mitigates finite-size effects, and employs active learning to optimize sampling in the volume-temperature space. It applies seamlessly to both crystalline and liquid phases. We demonstrate the methodology by computing heat capacities, thermal expansion, isothermal and adiabatic bulk moduli, and melting properties for nine elemental FCC and BCC metals using 20 classical and machine-learned interatomic potentials, with all predictions accompanied by quantified confidence intervals. Automated, general, and uncertainty-aware, the workflow advances high-throughput thermodynamics and provides a systematic benchmark for interatomic potentials.

Figures (14)

• Figure 1: Workflow for computing thermodynamic properties. MD simulations at each $(T, V)$ point provide mean energy $\langle E \rangle$ and pressure $\langle P \rangle$, which are fitted using Gaussian Process Regression (accounting for free energy asymptotics). The resulting $F_{\text{MD}}(T, V)$ is corrected for zero-point energy, and thermodynamic properties follow from its derivatives. Our Bayesian approach also allows us to optimally select the next simulation point via active learning.
• Figure 2: Equilibrium volume for FCC aluminum as a function of temperature, with and without the ZPE correction. Values are shown with $2\sigma$ confidence intervals obtained from the GPR model; for $V_{\mathrm{eq}}(T)$ these intervals are of the order $10^{-3}$ and therefore not visible.
• Figure 3: Linear thermal expansion coefficient for FCC aluminum. Classical MD predictions and ZPE-corrected values for the solid phase are compared with experimental data from touloukian1977_alpha. The shaded region indicates the $2\sigma$ confidence interval of the predictions.
• Figure 4: Temperature dependence of the constant-pressure heat capacity for FCC aluminum. Classical MD prediction (blue) and ZPE-corrected values (purple) for the solid phase are compared with experimental data from desai1987aluminium. The shaded region indicates the $2\sigma$ confidence interval of the predictions.
• Figure 5: Isothermal bulk modulus $K_T(T)$ of FCC aluminum. Classical MD predictions (blue) and ZPE-corrected values (purple) are compared with experimental data from tallon1979temperatureSutton. The shaded region indicates the $2\sigma$ confidence interval.