[Paper Review] Capturing long-range interaction with reciprocal space neural network

Hongyu Yu, Liangliang Hong+3 more|arXiv (Cornell University)|Nov 30, 2022

Machine Learning in Materials Science4 citations

TL;DR

This paper proposes a reciprocal space neural network (RSNN) framework that extends machine learning interatomic potentials to capture long-range interactions—such as Coulomb and van der Waals forces—by transforming real-space atomic configurations into reciprocal space. The method preserves Euclidean and translational invariance, enabling accurate modeling of global properties like band gaps in ionic systems, with demonstrated improvements in NaCl and defective GaxNy systems.

ABSTRACT

Machine Learning (ML) interatomic models and potentials have been widely employed in simulations of materials. Long-range interactions often dominate in some ionic systems whose dynamics behavior is significantly influenced. However, the long-range effect such as Coulomb and Van der Wales potential is not considered in most ML interatomic potentials. To address this issue, we put forward a method that can take long-range effects into account for most ML local interatomic models with the reciprocal space neural network. The structure information in real space is firstly transformed into reciprocal space and then encoded into a reciprocal space potential or a global descriptor with full atomic interactions. The reciprocal space potential and descriptor keep full invariance of Euclidean symmetry and choice of the cell. Benefiting from the reciprocal-space information, ML interatomic models can be extended to describe the long-range potential including not only Coulomb but any other long-range interaction. A model NaCl system considering Coulomb interaction and the GaxNy system with defects are applied to illustrate the advantage of our approach. At the same time, our approach helps to improve the prediction accuracy of some global properties such as the band gap where the full atomic interaction beyond local atomic environments plays a very important role. In summary, our work has expanded the ability of current ML interatomic models and potentials when dealing with the long-range effect, hence paving a new way for accurate prediction of global properties and large-scale dynamic simulations of systems with defects.

Motivation & Objective

• To address the limitation of existing machine learning interatomic potentials in capturing long-range interactions such as Coulomb and van der Waals forces.
• To extend local ML models to incorporate full atomic interactions beyond immediate neighbors.
• To preserve Euclidean and translational invariance in the representation of atomic systems.
• To improve prediction accuracy of global electronic properties, such as band gaps, which depend on long-range electron correlation.
• To enable large-scale dynamic simulations of defective materials with accurate long-range interactions.

Proposed method

• Transform real-space atomic configurations into reciprocal space using Fourier transforms to encode long-range information.
• Construct a reciprocal space potential or global descriptor that captures full atomic interactions while maintaining invariance under lattice translations and rotations.
• Integrate the reciprocal space representation into existing local machine learning interatomic models without altering their architecture.
• Ensure invariance under Euclidean transformations by designing the reciprocal space representation to be independent of the unit cell choice.
• Use the global descriptor to represent the full electronic environment, enabling accurate prediction of long-range effects.
• Train the model on systems with long-range interactions, such as NaCl and defective GaxNy, to validate performance.

Experimental results

Research questions

• RQ1 Can a machine learning interatomic potential be extended to accurately model long-range Coulomb interactions in ionic materials?
• RQ2 How can long-range atomic interactions be encoded in a way that preserves translational and rotational invariance?
• RQ3 To what extent does incorporating reciprocal space information improve the prediction of global electronic properties like the band gap?
• RQ4 Can the proposed method be seamlessly integrated into existing local interatomic potential frameworks?
• RQ5 Does the inclusion of long-range effects enhance the accuracy of simulations involving defects in materials?

Key findings

• The reciprocal space neural network successfully captures long-range interactions, including Coulomb forces, in ionic systems such as NaCl.
• The method improves the prediction accuracy of the band gap in materials where long-range electron correlation is critical.
• The global descriptor based on reciprocal space maintains full invariance under Euclidean transformations and unit cell choice.
• The approach enhances simulation accuracy for defective systems like GaxNy, where long-range interactions influence defect formation and electronic structure.
• The framework is compatible with existing local machine learning interatomic models, enabling broad applicability without architectural overhaul.
• The model demonstrates improved performance in predicting global properties that depend on full atomic interaction, not just local environments.