When do machine-learning potentials need a configuration-dependent kernel? Learning long-range interactions with Fourier neural operators
Abstract
Long-range interactions in machine-learning interatomic potentials are commonly treated by coupling learned sources through either a prescribed electrostatic kernel or a learned but configuration-independent one. Whether such a kernel suffices depends on the underlying screened interaction. We address this question by using Fourier neural operators (FNOs) to learn how latent source fields, built from the descriptors of a local backbone (here MACE), interact across the simulation cell. For a synthetic ionic system with tunable screening, a prescribed Coulomb kernel underestimates the long-wavelength charge fluctuations by 43% under strong screening, whereas the FNO reproduces them within 3% and recovers 95-99% of the variance of the residual left by the local backbone. A linear FNO, which learns a configuration-independent kernel, performs equally well in the homogeneous case. Under inhomogeneous screening, rearranging the remote medium modulates the coupling between distant ions, a dependence that no configuration-independent kernel can represent. Among the models tested, only the nonlinear FNO responds to this modulation, and its force errors are 27-41% lower than those of configuration-independent models. In first-principles benchmarks of liquid water, lithium lanthanum zirconate, and Au2/MgO(001), MACE-FNO is comparable to a prescribed-kernel model for the bulk systems and more accurate for the interface. It further captures the reversal of the Au2 wetting preference induced by remote Al dopants, with deviations below 5 meV per cell from density functional theory. These results indicate that a configuration-dependent kernel, as learned by FNOs, becomes necessary once the screening medium varies, even though the energy remains quadratic in the charges for a fixed medium.
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BibTeX
@misc{chen2026when,
title = {{When do machine-learning potentials need a configuration-dependent kernel? Learning long-range interactions with Fourier neural operators}},
author = {Wei Chen and Gian-Marco Rignanese},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.03678},
eprint = {2611.03678},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.03678},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - When do machine-learning potentials need a configuration-dependent kernel? Learning long-range interactions with Fourier neural operators
AU - Wei Chen
AU - Gian-Marco Rignanese
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.03678
UR - https://arxiv.org/abs/2611.03678
AB - Long-range interactions in machine-learning interatomic potentials are commonly treated by coupling learned sources through either a prescribed electrostatic kernel or a learned but configuration-independent one. Whether such a kernel suffices depends on the underlying screened interaction. We address this question by using Fourier neural operators (FNOs) to learn how latent source fields, built from the descriptors of a local backbone (here MACE), interact across the simulation cell. For a synthetic ionic system with tunable screening, a prescribed Coulomb kernel underestimates the long-wavelength charge fluctuations by 43% under strong screening, whereas the FNO reproduces them within 3% and recovers 95-99% of the variance of the residual left by the local backbone. A linear FNO, which learns a configuration-independent kernel, performs equally well in the homogeneous case. Under inhomogeneous screening, rearranging the remote medium modulates the coupling between distant ions, a dependence that no configuration-independent kernel can represent. Among the models tested, only the nonlinear FNO responds to this modulation, and its force errors are 27-41% lower than those of configuration-independent models. In first-principles benchmarks of liquid water, lithium lanthanum zirconate, and Au2/MgO(001), MACE-FNO is comparable to a prescribed-kernel model for the bulk systems and more accurate for the interface. It further captures the reversal of the Au2 wetting preference induced by remote Al dopants, with deviations below 5 meV per cell from density functional theory. These results indicate that a configuration-dependent kernel, as learned by FNOs, becomes necessary once the screening medium varies, even though the energy remains quadratic in the charges for a fixed medium.
ER -