Bayesian Free-Energy Reconstruction from Molecular Dynamics Accurately Predicts Thermodynamic Properties and Phase Stability

Predicting the thermodynamic properties of materials accurately remains a significant challenge, yet understanding these properties is crucial for designing new materials and predicting their behaviour. Ekaterina Spirande from the Moscow Institute, Timofei Miryashkin, and Andrei Kolmakov, alongside their colleagues, now present a new automated workflow that overcomes limitations in existing methods. Their approach reconstructs the Helmholtz free-energy surface from molecular dynamics data using advanced statistical techniques, effectively capturing both crystalline and liquid phases and accounting for uncertainties in the calculations. This achievement provides a systematic way to benchmark interatomic potentials and enables high-throughput prediction of essential material properties, such as heat capacity and thermal expansion, with quantified confidence intervals, representing a substantial advance in computational materials science.

Gaussian Processes Quantify Thermodynamic Uncertainty

Scientists developed a method for quantifying uncertainty in thermodynamic properties using Gaussian process regression and perturbation theory. This approach models the free energy of a system, allowing for the calculation of variances in properties like bulk modulus and adiabatic bulk modulus. By combining these tools, researchers accurately estimate the uncertainty associated with thermodynamic predictions. The method expresses thermodynamic properties as derivatives of the free energy, expanding these derivatives around a reference state. This linearization allows for the calculation of variances based on the variance of the free energy and the sensitivity of the property to changes in free energy, providing a robust framework for understanding and quantifying uncertainty in thermodynamic calculations.

Free Energy Reconstruction via Gaussian Process Regression

Scientists engineered a novel workflow for calculating free energy, a crucial property for predicting material behaviour. Recognizing the limitations of traditional methods, the team combined the strengths of phonon-based approaches and molecular dynamics simulations, pioneering the use of Gaussian Process Regression to reconstruct the Helmholtz free-energy surface directly from irregularly sampled molecular dynamics trajectories, effectively capturing anharmonic contributions to the energy. To account for quantum effects at low temperatures, researchers augmented the reconstruction with zero-point energy corrections. This innovative combination allows for accurate free-energy calculations across a wide range of temperatures and phases, including both crystalline solids and liquids. The workflow systematically propagates statistical uncertainties, providing quantified confidence intervals for all predictions, and implements active learning techniques to optimize sampling, maximizing calculation efficiency and accuracy. This methodology was demonstrated by computing key thermodynamic properties for nine elemental metals, providing a comprehensive benchmark for assessing interatomic potentials and accelerating materials design.

Free Energy Calculations with Enhanced Accuracy and Efficiency

Scientists have developed a new workflow for accurately calculating the free energy of materials, a crucial step in predicting their properties and stability. This research presents a unified approach that combines the strengths of molecular dynamics simulations with Gaussian Process Regression, offering a robust and efficient solution for both crystalline solids and liquids. The team reconstructed the Helmholtz free-energy surface from molecular dynamics data, incorporating corrections for zero-point energy derived from harmonic and quasi-harmonic theory. This method propagates statistical uncertainties, mitigating the effects of finite system sizes and employing active learning to optimize sampling across different volumes and temperatures. Experiments demonstrate the workflow’s ability to compute key thermodynamic properties, including heat capacity, thermal expansion, and bulk moduli, for nine elemental metals, providing a systematic benchmark for interatomic potentials and advancing high-throughput materials modeling and materials discovery.

Free Energy Prediction via Machine Learning

This research presents a new workflow for accurately calculating the Helmholtz free energy of materials, a crucial property for predicting stability and behaviour. This work overcomes the limitations of traditional methods by combining molecular dynamics with Gaussian Process Regression, a powerful machine learning technique, to reconstruct the free energy surface. The method incorporates corrections for zero-point energy, improving accuracy, and propagates statistical uncertainties to provide reliable predictions. The team demonstrated the effectiveness of this approach by calculating a range of thermodynamic properties, including heat capacity, thermal expansion, and bulk moduli, for nine common metals, providing a systematic benchmark for evaluating interatomic potentials. The workflow is applicable to both crystalline solids and liquids, and automates a process previously requiring substantial manual effort, representing a significant step towards high-throughput materials discovery and a more reliable prediction of material properties.