EquiFiLM: Charge-Conditioned Equivariant Force Fields via Feature-wise Linear Modulation

2026-07-06

AI Summary

Current machine learning force fields struggle to natively model electronic state changes induced by external perturbations such as charges or electric fields, limiting their applicability to nonequilibrium processes. This work proposes a lightweight, backbone-agnostic Feature-wise Linear Modulation (FiLM) extension that introduces continuous external conditioning into any E(3)-equivariant force field by modulating only scalar channels, while preserving equivariance. The approach seamlessly integrates with architectures featuring scalar interaction layers—such as MACE-MatPES—and efficiently learns the influence of external fields on potential energy surfaces with minimal data. In charged liquid water systems, the method reduces force and energy RMSE by factors of 3.1 and 61, respectively, compared to non-FiLM baselines, maintains high accuracy across seven unseen charge states, and enables stable molecular dynamics simulations.

Abstract

Foundation machine learning force fields (MLFFs) such as MACE-MP-0 and UMA cover broad chemical space at near density functional theory (DFT) accuracy. However, they assume equilibrium ground-state physics and do not natively handle externally induced changes to the electronic state, such as charging, applied fields, or electronic excitation, which limits their use for driven processes such as photoexcitation and charge injection. We propose EquiFiLM, a lightweight extension that adds continuous external conditioning to any equivariant foundation MLFF via a per-layer Feature-wise Linear Modulation (FiLM) block, learning externally driven changes to the potential energy surface from minimal training data. The block modulates only scalar channels and preserves E(3)-equivariance exactly. We demonstrate the recipe on charged liquid water with the foundation model MACE-MatPES as the backbone, yielding E-MACE. On the four training charges, E-MACE delivers a $3.1\times$ reduction in force RMSE ($21.3$ to $6.96$ meV/$\mathring{A}$) and a $61\times$ reduction in per-atom energy RMSE ($6.1$ to $0.1$ meV/atom) over a baseline without EquiFiLM trained on the same data, at indistinguishable inference cost. Across seven held-out interpolation and extrapolation charges, force RMSE stays within $18-61$ meV/$\mathring{A}$ and energy RMSE within $0.7-5.4$ meV/atom. The model runs stable molecular dynamics across the full range tested and predicts the charge-dependent first-shell response of the reduced pair distribution function probed by ultrafast electron diffraction. Adding this conditioning axis to the foundation requires only a few thousand DFT-labeled frames, against the $\approx 10^8$ structures of a charge-aware foundation trained from scratch. The recipe is backbone- and conditioning-agnostic: it applies without architectural change to any equivariant MLFF with scalar interaction-layer channels.

Problem

• machine learning force fields
• electronic excitation
• charging
• equivariance
• non-equilibrium processes

Innovation

• Equivariant MLFF
• Feature-wise Linear Modulation
• Charge Conditioning
• Potential Energy Surface
• External Field Response