Unified Representation of Molecules and Crystals for Machine Learning (1704.06439v4)

Abstract: Accurate simulations of atomistic systems from first principles are limited by computational cost. In high-throughput settings, machine learning can reduce these costs significantly by accurately interpolating between reference calculations. For this, kernel learning approaches crucially require a representation that accommodates arbitrary atomistic systems. We introduce a many-body tensor representation that is invariant to translations, rotations, and nuclear permutations of same elements, unique, differentiable, can represent molecules and crystals, and is fast to compute. Empirical evidence for competitive energy and force prediction errors is presented for changes in molecular structure, crystal chemistry, and molecular dynamics using kernel regression and symmetric gradient-domain machine learning as models. Applicability is demonstrated for phase diagrams of Pt-group/transition-metal binary systems.

• The paper presents MBTR, a novel many-body tensor representation that lowers QM simulation costs using machine learning.
• It demonstrates high predictive accuracy, achieving MAEs below 1 kcal/mol for molecules and RMSE of 8.1 meV/atom for crystals.
• The methodology ensures invariance to translations, rotations, and permutations, enabling efficient high-throughput materials discovery.

Overview of "Unified Representation of Molecules and Crystals for Machine Learning"

The paper, "Unified Representation of Molecules and Crystals for Machine Learning," by Haoyan Huo and Matthias Rupp, introduces a novel many-body tensor representation (MBTR) for atomistic systems. This representation is specifically designed to facilitate the reduction of computational costs associated with quantum mechanical (QM) simulations through the use of ML. This paper targets a problem of substantial import: the high computational demand of first-principles methods. The authors present a solution that accommodates the diverse and arbitrary nature of molecular and crystal structures, proposing a representation that is invariant to translations, rotations, and permutations of nuclei with identical elements.

Methodology

The authors develop the MBTR by advancing beyond traditional representations like Coulomb matrices and introducing a framework that leverages many-body expansions. This tensor-based representation effectively encodes atomistic configurations by structuring atomic interactions through stratification by element type while preserving essential symmetry properties. The key attributes of MBTR include its invariance to symmetrical transformations and its unique characterization of atomic environments, essential for robust machine learning applications.

Key Results

The practical utility and accuracy of MBTR are confirmed through several empirical evaluations involving:

• Molecular Configurations: The representation's efficacy is demonstrated across a dataset comprising 7,211 organic molecules, where machine learning models achieved mean absolute errors (MAEs) below 1 kcal/mol for atomization energies using only 5,000 training samples.
• Crystalline Materials: MBTR was applied to data involving 11,000 elpasolite crystal structures, yielding a RMSE of 8.1 meV/atom—a strong indicator of its predictive precision across varying crystal chemistries.
• Dynamical Simulations: The model's performance was benchmarked with respect to dynamic changes in molecular geometry, achieving competitive energy and force prediction accuracies.
• Phase Diagrams: MBTR facilitated the identification of stable and metastable phases in Pt-group/transition metal binary systems with significant computational savings.

Implications and Future Directions

The potential applications of MBTR extend beyond those demonstrated within this paper. The efficiency of the representation in combining physical and chemical insights with machine learning opens pathways for its integration into high-throughput materials discovery platforms. Given its generalizable framework, future research could explore its adaptability to other classes of materials and complex chemical environments, potentially optimizing the prediction of electronic, optical, and thermodynamic properties.

Conclusion

The paper presents a thorough approach to bridging the gap between computational chemistry and machine learning through an innovative tensor representation. Its implications are broad-ranging, promoting efficient data-driven models that could significantly transform computational practices in materials science and chemistry. Future work is likely to extend MBTR's application scope, supporting the ongoing fusion of machine learning with fundamental chemical theory to unlock new efficiencies in materials discovery and development.