General Learning of the Electric Response of Inorganic Materials

Dielectric response governs how materials interact with electric fields and light. Still, first-principles prediction of polarization <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mi mathvariant="bold">P</a:mi> </a:math> , Born effective charges <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:msup> <c:mi>Z</c:mi> <c:mo>*</c:mo> </c:msup> </c:math> , and polarizability <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:mrow> <d:mi mathvariant="bold-italic">α</d:mi> </d:mrow> </d:math> remains too costly for large-scale screening and long-time dynamics. We introduce , a field-aware, <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"> <f:mrow> <f:mi>O</f:mi> <f:mo>(</f:mo> <f:mn>3</f:mn> <f:mo>)</f:mo> </f:mrow> </f:math> -equivariant interatomic potential that learns a single electric-enthalpy functional <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"> <g:mrow> <g:mi mathvariant="script">F</g:mi> <g:mo>(</g:mo> <g:mo>{</g:mo> <g:mi mathvariant="bold">R</g:mi> <g:mo>}</g:mo> <g:mo>,</g:mo> <g:mi mathvariant="bold">E</g:mi> <g:mo>)</g:mo> </g:mrow> </g:math> and obtains <k:math xmlns:k="http://www.w3.org/1998/Math/MathML"> <k:mi mathvariant="bold">P</k:mi> <k:mo>,</k:mo> <k:mo> </k:mo> <k:msup> <k:mi>Z</k:mi> <k:mo>*</k:mo> </k:msup> </k:math> , and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi mathvariant="bold-italic">α</m:mi> </m:mrow> </m:math> by exact differentiation. A uniform field couples to latent equivariant features inside the 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 , existing energy/force foundation models can be upgraded to become field aware. Benchmarked against semilocal density-functional theory (DFT)/density-functional perturbation theory (DFPT) reference data, a directly trained cross-chemistry ferroelectric model reproduces the same-branch Berry phase and spontaneous polarizations across diverse inorganic crystals. Starting from the multihead foundation model and its Open Materials 2024 (OMAT)-Perdew-Burke-Ernzerhof (PBE) head, joint fine-tuning on dielectric, ferroelectric, and replay data yields foundation models, which predict <o:math xmlns:o="http://www.w3.org/1998/Math/MathML"> <o:msup> <o:mi>Z</o:mi> <o:mo>*</o:mo> </o:msup> <o:mo>,</o:mo> <o:mo> </o:mo> <o:mrow> <o:mi mathvariant="bold-italic">α</o:mi> </o:mrow> </o:math> , derived dielectric constants, and cross-chemistry polarization trends with fidelity that captures branch-resolved polarization and spontaneous polarization, while retaining strong force-field accuracy. Further, single-material models and reproduce <q:math xmlns:q="http://www.w3.org/1998/Math/MathML"> <q:msub> <q:mi>BaTiO</q:mi> <q:mn>3</q:mn> </q:msub> </q:math> hysteresis loops and <r:math xmlns:r="http://www.w3.org/1998/Math/MathML"> <r:mi>α</r:mi> </r:math> -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.