Latent Ewald summation for machine learning of long-range interactions

Aug 3, 2026

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Machine learning interatomic potentials often omit long-range interactions such as electrostatics and dispersion, leading to inaccurate or unphysical behavior when such effects become important. This work presents Latent Ewald Summation (LES), which learns a hidden variable from local atomic descriptors and evaluates the long-range contribution via an Ewald summation. Benchmarks across charged and polar molecular dimers, bulk water, and water–vapor interfaces show that LES removes artifacts produced by standard short-ranged MLIPs with only about twice the computational cost.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages8

Reading Time20 min

AccessFree to download

Abstract

Results

Theory

Method

Short-range energy decomposition

Hidden-variable representation

Structure factor and long-range energy

npj | computational materials Article Published in partnership with the Shanghai Institute of Ceramics of the Chinese Academy of Sciences [https://doi.org/10.1038/s41524-025-01577-7](https://doi.org/10.1038/s41524-025-01577-7) Latent Ewald summation for machine learning of long-range interactions Check for updates | Bingqing Cheng1,2 | | | --- | --- | | Machine learning interatomic potentials (MLIPs) often neglect long-range interactions, such as electrostatic and dispersion forces. In this work, we introduce a straightforward andefﬁcient method to account for long-range interactions by learning a hidden 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. | | | Machine learning interatomic potentials (MLIPs) can learn from reference quantum mechanical calculations and then predict the energy and forces of atomic conﬁgurations quickly, allowing for a more accurate and comprehensive exploration of material and molecular properties at scale1,2. Most state-of-the-art MLIP methods use a short-range approximation: the effective potential energy surface experienced by one atom is determined by its atomic neighborhood. This approximation implies that the total energy is the sum of atomic contributions, which also makes the MLIPs scale linearly with system size.
The short-range MLIPs, however, neglect all kinds of long-range interactions, such as Coulomb and dispersion. Although short-range potentials may be sufﬁcient to describe most properties of homogeneous bulk systems3, they may fail for liquid-vapor interfaces4, dielectric response5,6, dilute ionic solutions with Debye-Hückel screening, and interactions between gas phase molecules7.
There has been a continuous effort to incorporate long-range interactions into MLIPs. One can include empirical electrostatics and dispersion baseline corrections4,8,9, but for many systems, such baseline is not readily available. Another option is to predict effective partial charges to each atom, which are then used to calculate long-range electrostatics10–15. For example, the fourth-generation high-dimensional neural network potential (4GHDNNPs)11 predicts the electronegativities of each nucleus and then use a charge equilibration scheme16 to assign the charges. 4G-HDNNPs are trained directly to reproduce atomic partial charges from reference quantum mechanical calculations, although partial charges are not physically observable and their values depend on the speciﬁc partitioning scheme used13. In a similar vein, the deep potential long-range (DPLR)17 learns maximally localized Wannier function centers (MLWFCs) for insulating systems, and the self-consistentﬁeld neural network(SCFNN)12 predicts the electronic response via the position of the MLWFCs. Message passing neural networks (MPNNs)18–21 employ a number of graph convolution layers to communicate information between atoms, thus capturing long- | range interaction up to the local cutoff radius times the number of layers. However, if parts of the system are disconnected on the graph, e.g. two molecules with a distance beyond the cutoff, the message passing scheme does not help. Another class of methods is to learn the long-range descriptors and interactions in the reciprocal space with learnable frequency ﬁlters22,23. Finally, a very interesting approach is the long-distance equivariant (LODE) method7,24, which uses local descriptors to encode the Coulomband other asymptotic decaying potentials(1/rp)around the atoms, anda related, density-based long-range descriptors25.
Here, we propose a simple method, the Latent Ewald Summation (LES), for account

FAQs

Why do standard short-range MLIPs fail for long-range physics?

They use a short-range neighborhood approximation, so they neglect long-range interactions such as Coulomb electrostatics and dispersion. This can produce unphysical predictions in systems where long-range effects matter.

How does Latent Ewald Summation (LES) incorporate long-range interactions?

LES learns a hidden variable from invariant local atomic descriptors, constructs its structure factor in reciprocal space, and then computes the long-range energy using an Ewald summation form that captures the electrostatic potential.

What systems were used to benchmark LES, and what was the cost impact?

The method was benchmarked on charged and polar molecular dimers, bulk water, and water–vapor interfaces. Long-range modeling largely removes artifacts while using only about twice the computational cost of short-range MLIPs.

Aug 3, 2026

Upload by Skyler