Scalable long-range machine learning interatomic potentials with electrical response for atomistic material modeling

Yicheng Chen; Xiaoyun Yu; Hyejeong Song; Xintian Wang; Zihui Li; Zixi Xia; Junmin Chen; Peichen Zhong

cond-mat.mtrl-sciOct 16, 2026

Scalable long-range machine learning interatomic potentials with electrical response for atomistic material modeling

Authors: Yicheng Chen, Xiaoyun Yu, Hyejeong Song, Xintian Wang, Zihui Li, Zixi Xia, Junmin Chen, Peichen Zhong

Organizations: Department of Materials Science and Engineering, National University of Singapore, Singapore · Department of Physics, National University of Singapore, Singapore

Abstract

Accurate atomistic simulations of materials under electric fields require long-range electrostatics and electrical-response modeling at length scales beyond the reach of conventional first-principles methods. Yet these capabilities remain difficult to reconcile with the scalability of machine-learning interatomic potentials (MLIPs). Strictly local models enable efficient spatial parallelization but neglect long-range interactions, whereas existing electrostatic extensions introduce global dependencies that hinder distributed computation. Here, we overcome this limitation by analytically separating the long-range electrostatic forces and Born effective charges (BECs) into a global electrostatics calculation and strictly local derivatives of learned latent charges. This formulation preserves the spatial decomposability of equivariant MLIPs while enabling distributed evaluation of energies, forces, stresses, and BECs across different boundary conditions. Implemented as DPA4C-LR on the nvalchemi platform, the framework scales to 5.2 million atoms on four GPUs at approximately twice the computational cost of its short-range backbone. Trained on energies and forces, DPA4C-LR accurately infers BECs and reproduces the field-dependent infrared spectra of water. We further demonstrate its capabilities by recovering the characteristic slim polarization hysteresis of relaxor \ce{Pb(Mg_{1/3}Nb_{2/3})O3}, which is obscured by finite-size effects in smaller simulations; predicting a room-temperature field-driven ionic conductivity of $6.8 \pm 0.7$ ~mS/cm in amorphous \ce{Li_{0.9}NbO_{0.9}Cl_{4.1}}; and modeling interfacial thermal transport across Si/diamond interfaces with slab-corrected electrostatics. By combining long-range physics, electrical-response inference, and distributed computation, this framework extends predictive atomistic modeling toward device-relevant length scales.

Figures & tables

Figure 1: Schematic of the distributed workflow for evaluating energies, forces, and Born effective charges (BECs) with strictly local models augmented by long-range electrostatics. Local models predict per-atom short-range energies and raw charges on each partition. A global Ewald/PME step, implemented with the NVIDIA ALCHEMI Toolkit-Ops, then enforces the total-charge constraint and evaluates the long-range energy and its derivatives, while local automatic differentiation provides the remaining position derivatives. These contributions are assembled into the total energy, forces, and BECs.

Figure 2: DPA4C-LR for bulk water. (a)–(c) Test-set RMSEs of energies, forces, and BECs for DPA4C, DPA4C-LR, and the M1 and M2 variants of qNEP. (d) Diagonal BECs ( $Z^{*}_{\alpha\alpha}$ ) predicted by DPA4C-LR against DFPT reference values, with the off-diagonal components ( $Z^{*}_{\alpha\beta}$ ) in the inset. (e) Simulated IR spectra of bulk water under static electric fields of 0–0.15 V/Å, compared with experiment [ 11 ] . (f)–(h) Time per MD step against number of atoms on one, two, and four NVIDIA H200 GPUs for DPA4C, DPA4C-LR, and DPA4C-LR with on-the-fly BEC evaluation.

Figure 3: DPA4C-LR for relaxor PMN. (a) $18\times 18\times 18$ PMN supercell from FIRE-Swap, showing only the B sites, with Nb in blue and Mg in red. (b) Ratio of Nb sites in all Nb clusters (black) and in the largest cluster (navy) against the number of MC swap iterations. The insets show the largest cluster after 0, $7\times 10^{4}$ , and $1.4\times 10^{5}$ iterations. (c) Diagonal BECs ( $Z^{*}_{\alpha\alpha}$ ) predicted by DPA4C-LR against DFPT, with the off-diagonal components ( $Z^{*}_{\alpha\beta}$ ) in the inset. (d)–(f) $P$ – $\mathcal{E}$ loops along [111] at 300 K for $6\times 6\times 6$ , $12\times 12\times 12$ , and $18\times 18\times 18$ supercells. Red lines give the mean over replicas, and gray lines give the individual replicas.

Figure 4: DPA4C-LR for amorphous LNOC. (a) Training and held-out frames in each configuration family. (b) Force and energy RMSEs of DPA4C-LR and the short-range DPA4C on the held-out frames, by family. (c) Neutron-weighted $G(r)$ of a 2,236-atom glass quenched with MACE-MH-1 and with DPA4C-LR. (d) One of the four 19,872-atom glasses quenched with DPA4C-LR. (e) Charge displacement $D(t)$ at 300 K under static electric fields. Colored lines give the component along the field, averaged over the four glasses, with a band of one standard error between glasses. The black line gives the component along $x$ without a field (zero field), and gray lines give the components perpendicular to the field. The legend gives the physical field $\mathcal{E}$ (labeled $E_{0}$ in the plot) and the conductivity with its 95% confidence interval over 100 ps blocks of the 500–1000 ps window.

Figure 5: (a) NEMD setup for the 11 nm Si/diamond interface. (b) Temperature profile from one representative production run, with linear extrapolations to determine the interfacial temperature drop

\Delta T_{\mathrm{int}}

. (c) Cumulative energy exchanged with the thermostats in the same run, from which the heat flux

J

is obtained. (d) Long-range electrostatic energy of the 32 nm cell as a function of vacuum gap, comparing direct 2D Ewald summation with uncorrected and Yeh–Berkowitz-corrected 3D Ewald summation. The dotted line marks the production vacuum gap of 40.3 Å; the inset shows the maximum absolute deviation from the 2D reference.

Figure 6: Diagonal BECs (

Z^{*}_{\alpha\alpha}

) of Nb in a 15-atom

\text{Pb}{\vphantom{\text{X}}}_{\smash[t]{\text{3}}}\text{(}\text{Mg}{\vphantom{\text{X}}}_{\smash[t]{\text{1}}}\text{Nb}{\vphantom{\text{X}}}_{\smash[t]{\text{2}}}\text{)}\text{O}{\vphantom{\text{X}}}_{\smash[t]{\text{9}}}

cell repeated

n\times n\times n

, normalized to

n=12

, from Eq. ( 10 ) for DPA4C-LR and from Eq. ( 15 ) for CACE-LR with LES.

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William J. Baldwin, Ilyes Batatia, Martin Vondrák, Johannes T. Margraf+1

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Density Functional Theory Machine Learning Interatomic Potentials Computational Materials Science

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Machine learning interatomic potentials (MLIPs) have become widely used tools in atomistic simulations. For much of the history of this field, the most commonly employed architectures were based on short-ranged atomic energy contributions, and the assumption of locality still persists in many modern foundation models. While this approach has enabled efficient and accurate modelling for many use cases, it poses intrinsic limitations for systems where long-range electrostatics, charge transfer, or induced polarization play a central role. A growing body of work has proposed extensions that incorporate electrostatic effects, ranging from locally predicted atomic charges to self-consistent models. While these models have demonstrated success for specific examples, their underlying assumptions, and fundamental limitations are not yet well understood. In this work, we present a framework for treating electrostatics in MLIPs by viewing existing models as coarse-grained approximations to density functional theory (DFT). This perspective makes explicit the approximations involved, clarifies the physical meaning of the learned quantities, and reveals connections and equivalences between several previously proposed models. Using this formalism, we identify key design choices that define a broader design space of self-consistent electrostatic MLIPs. We implement salient points in this space using the MACE architecture and a shared representation of the charge density, enabling controlled comparisons between different approaches. Finally, we evaluate these models on two instructive test cases: metal-water interfaces, which probe the contrasting electrostatic response of conducting and insulating systems, and charged vacancies in silicon dioxide. Our results highlight the limitations of existing approaches and demonstrate how more expressive self-consistent models are needed to resolve failures.

Abstract

Machine Learning Interatomic Potentials

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