Polarizable atomic multipoles for learning long-range electrostatics

Long-range electrostatics and polarization remain central obstacles to extending machine learning interatomic potentials (MLIPs) to ionic, polar, and interfacial systems. Here, we introduce a semi-local framework for learning electrostatics from energies and forces using polarizable atomic multipoles. Local equivariant descriptors predict environment-dependent latent monopoles, dipoles, and quadrupoles, while residual non-local charge transfer and polarization are captured by non-self-consistent linear response in induced charges and dipoles. Across four diverse benchmarks and four short-range MLIP architectures, the multipole hierarchy and response terms systematically improve potential energy surface accuracy, with the largest gains in systems where long-range effects are essential. More importantly, the learned latent variables recover physically meaningful electrical responses: accurate Born effective charge tensors, emergent polarizabilities, infrared spectra in close agreement with experiments, and semi-quantitative Raman spectra for bulk water and hybrid MAPbI$_3$ perovskite. This systematically improvable, physically transparent framework enables MLIPs trained on standard energy and force labels to predict polarization-sensitive observables.

Machine learning interatomic potential can infer electrical response

Modeling the response of material and chemical systems to electric fields remains a longstanding challenge. Machine learning interatomic potentials (MLIPs) offer an efficient and scalable alternative to quantum mechanical methods but do not by themselves incorporate electrical response. Here, we show that polarization and Born effective charge (BEC) tensors can be directly extracted from long-range MLIPs within the Latent Ewald Summation (LES) framework, solely by learning from energy and force data. Using this approach, we predict the infrared spectra of bulk water under zero or finite external electric fields, ionic conductivities of high-pressure superionic ice, and the phase transition and hysteresis in ferroelectric PbTiO$_3$ perovskite. This work thus extends the capability of MLIPs to predict electrical response--without training on charges or polarization or BECs--and enables accurate modeling of electric-field-driven processes in diverse systems at scale.

Learning charges and long-range interactions from energies and forces

Accurate modeling of long-range forces is critical in atomistic simulations, as they play a central role in determining the properties of materials and chemical systems. However, standard machine learning interatomic potentials (MLIPs) often rely on short-range approximations, limiting their applicability to systems with significant electrostatics and dispersion forces. We recently introduced the Latent Ewald Summation (LES) method, which captures long-range electrostatics without explicitly learning atomic charges or charge equilibration. Extending LES, we incorporate the ability to learn physical partial charges, encode charge states, and the option to impose charge neutrality constraints. We benchmark LES on diverse and challenging systems, including charged molecules, ionic liquid, electrolyte solution, polar dipeptides, surface adsorption, electrolyte/solid interfaces, and solid-solid interfaces. Our results show that LES can effectively infer physical partial charges, dipole and quadrupole moments, as well as achieve better accuracy compared to methods that explicitly learn charges. LES thus provides an efficient, interpretable, and generalizable MLIP framework for simulating complex systems with intricate charge transfer and long-range