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Latent Ewald summation for machine learning of long-range interactions

Bingqing Cheng

TL;DR

This work introduces Latent Ewald Summation (LES), a simple, generically compatible method to incorporate long-range interactions into ML interatomic potentials by mapping local descriptors to a latent variable q_i and applying an Ewald sum over the resulting structure factor S(k). LES enables long-range communication and accurate treatment of electrostatics and dielectric effects without relying on explicit partial charges or Wannier centers, incurring roughly double the cost of short-range models. Across molecular dimers, molten NaCl, bulk water, and water–vapor interfaces, LES consistently outperforms purely short-range approaches, especially in properties tied to long-range physics such as dipole correlations and interfacial screening. The approach is lightweight, easily integrates with existing MLIP architectures, and promises broad applicability to systems with significant electrostatic or dielectric character.

Abstract

Machine learning interatomic potentials (MLIPs) often neglect long-range interactions, such as electrostatic and dispersion forces. In this work, we introduce a straightforward and efficient method to account for long-range interactions by learning a latent variable from local atomic descriptors and applying an Ewald summation to this variable. We demonstrate that in systems including charged and polar molecular dimers, bulk water, and water-vapor interface, standard short-ranged MLIPs can lead to unphysical predictions even when employing message passing. The long-range models effectively eliminate these artifacts, with only about twice the computational cost of short-range MLIPs.

Latent Ewald summation for machine learning of long-range interactions

TL;DR

This work introduces Latent Ewald Summation (LES), a simple, generically compatible method to incorporate long-range interactions into ML interatomic potentials by mapping local descriptors to a latent variable q_i and applying an Ewald sum over the resulting structure factor S(k). LES enables long-range communication and accurate treatment of electrostatics and dielectric effects without relying on explicit partial charges or Wannier centers, incurring roughly double the cost of short-range models. Across molecular dimers, molten NaCl, bulk water, and water–vapor interfaces, LES consistently outperforms purely short-range approaches, especially in properties tied to long-range physics such as dipole correlations and interfacial screening. The approach is lightweight, easily integrates with existing MLIP architectures, and promises broad applicability to systems with significant electrostatic or dielectric character.

Abstract

Machine learning interatomic potentials (MLIPs) often neglect long-range interactions, such as electrostatic and dispersion forces. In this work, we introduce a straightforward and efficient method to account for long-range interactions by learning a latent variable from local atomic descriptors and applying an Ewald summation to this variable. We demonstrate that in systems including charged and polar molecular dimers, bulk water, and water-vapor interface, standard short-ranged MLIPs can lead to unphysical predictions even when employing message passing. The long-range models effectively eliminate these artifacts, with only about twice the computational cost of short-range MLIPs.
Paper Structure (13 sections, 5 equations, 8 figures, 1 table)

This paper contains 13 sections, 5 equations, 8 figures, 1 table.

Table of Contents

  1. Results
  2. Theory
  3. Example on molecular dimers
  4. Example on molten NaCl
  5. Example on bulk water
  6. Example on interfacial water
  7. Discussion
  8. Methods
  9. Implementation
  10. Selection of the smearing factor $\sigma$
  11. Benchmark of inference speed
  12. MD of Bulk Water
  13. MD of Water Liquid-Vapor Interfaces

Figures (8)

  • Figure 1: Comparison of the short-range (SR) and long-range (LR) machine learning interatomic potential performance for three dimer classes: charged-charged (CC), charged-polar (CP), and polar-polar (PP). For each class, the upper panel shows a snapshot of the system with the charge states indicated, the middle panel shows the parity plot for the force components, and the lower panel shows the binding energy curve, which is the potential energy difference between the dimer, and two isolated and relaxed monomers. The root mean square errors (RMSE) for the energy and force components of the test sets are shown in the insets.
  • Figure 2: Learning curves of energy ($E$) and force ($F$) mean absolute errors (MAEs) on the bulk water dataset cheng2019ab, using short-range (SR) or long-range (LR) models and with or without massage passing layers ($T=0$ or $T=1$).
  • Figure 3: Predicted oxygen-oxygen radial distribution functions (RDF) of water at 300 K and 1 g/mL, using short-range (SR) or long-range (LR) models and with or without massage passing layers ($T=0$ or $T=1$). The experimental O-O RDF at ambient conditions was obtained from Ref skinner2014structure.
  • Figure 4: Predicted dipole density correlations in reciprocal space, using short-range (SR) or long-range (LR) models and with or without massage passing layers ($T=0$ or $T=1$). The inset shows a zoom-in of the small $k$ values.
  • Figure 5: Learning curves on the liquid–vapor water interface dataset niblett2021learning using the short-range (SR) and long-range (LR) models with no message passing ($T=0$) or one message passing layers ($T=1$).
  • ...and 3 more figures