General Learning of the Electric Response of Inorganic Materials

2025/08/25 by Bradley A. A. Martin, Martin, Bradley A. A., Alex M. Ganose +7 · 3 citations
Physics and Astronomy · #FOS: Physical sciences #Materials Science (cond-mat.mtrl-sci) #cond-mat.mtrl-sci

paper · pdf · doi:10.48550/arxiv.2508.17870

published as PRX Intelligence 1, 013006 (2026) · 22 pages, 12 figures, 43 equations

arxiv created 2026/06/05 · arxiv updated 2026/07/31

Abstract

We introduce MACE-Field, a field-aware, O(3)-equivariant interatomic potential that learns a single electric enthalpy functional \mathcal F(\\mathbf R\,\mathbf E) and obtains \mathbf P, Z^*, and \boldsymbolα by exact differentiation. A uniform field couples to latent equivariant features inside the MACE backbone, while the scalar energy readout preserves Maxwell reciprocity, the acoustic sum rule, and crystal tensor symmetries by construction. Because this coupling is a plug-in on top of standard MACE, existing energy/force foundation models can be upgraded to become field-aware. Benchmarked against semilocal DFT/DFPT reference data, a directly trained cross-chemistry ferroelectric model reproduces the same-branch Berry-phase and spontaneous polarisations across diverse inorganic crystals. Starting from the multihead foundation model mace-mp-mh-0 and its OMAT-PBE head, joint fine-tuning on dielectric, ferroelectric, and replay data yields MACE-Field-MH-0 foundation models, which predict Z^*, \boldsymbolα, derived dielectric constants, and cross-chemistry polarisation trends with fidelity that captures branch-resolved polarisation and spontaneous-polarisation, while retaining strong force-field accuracy. Further, single-material MACE-Field models and MACE-Field-MH-0 reproduce \ceBaTiO3 hysteresis loops and α-quartz infrared, Raman, and dielectric spectra from finite-field molecular dynamics, comparable to DFPT. These results show that a simple, physics-informed field coupling can endow atomistic foundation models with transferable dielectric and ferroelectric response, while targeted single-material training remains advantageous for the most quantitative spectroscopic predictions.

Citations

• Beyond Numerical Hessians: Higher-Order Derivatives for Machine Learning Interatomic Potentials via Automatic Differentiation
• Latent Ewald summation for machine learning of long-range interactions
• Unified Differentiable Learning of Electric Response
• A foundation model for atomistic materials chemistry
• MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fields
• Recent Progress in the Theory of Bulk Photovoltaic Effect
• E(3)-equivariant graph neural networks for data-efficient and accurate interatomic potentials
• Predicting molecular dipole moments by combining atomic partial charges and atomic dipoles
• Accurate molecular polarizabilities with coupled-cluster theory and machine learning
• Operators in quantum machine learning: Response properties in chemical space
• The atomic simulation environment—a Python library for working with atoms

Cited by

• A Cartesian-3j Framework for Machine Learning Interatomic Potentials
• Transient Detour and Cooperative Oxygen Exchange in the Polarization Switching of Ferroelectric Hf0.5Zr0.5O2
• Investigating Anharmonicities in Polarization-Orientation Raman Spectra of Acene Crystals with Machine Learning

Related

• Unified Differentiable Learning of Electric Response
• Machine learning interatomic potential can infer electrical response
• A foundation machine learning potential with polarizable long-range interactions for materials modelling
• Machine learning Landau free energy potentials
• Cross Learning between Electronic Structure Theories for Unifying Molecular, Surface, and Inorganic Crystal Foundation Force Fields