EquiFiLM: Charge-Conditioned Equivariant Force Fields via Feature-wise Linear Modulation
Authors: Samuel Sahel-Schackis, Ken-ichi Nomura, Aiichiro Nakano, Matthias F. Kling, Thomas Linker
Organizations: Department of Physics, Stanford University · Collaboratory for Advanced Computing and Simulation, University of Southern California · Linac Coherent Light Source, SLAC National Accelerator Laboratory · Stanford PULSE Institute, SLAC National Accelerator Laboratory
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× reduction in force RMSE (21.3 to 6.96 meV/A˚) and a 61× 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/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 ≈108 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.
Foundation machine learning interatomic potentials (MLIPs) have enabled atomistic simulations across broad regions of chemical and materials space, but many remain computationally expensive and lack explicit electrostatics, limiting their use for systems governed by long-range interactions and electrical response. Previously, we introduced Latent Ewald Summation (LES), which learns latent atomic charges and long-range electrostatics from density functional theory (DFT) energy and force labels alone. Here, we use LES to extract electrostatics that are latent in foundation models: energies and forces predicted by a teacher model are used to train a lightweight LES-augmented student MLIP, with optional fine-tuning on additional DFT data. The resulting models reduce computational cost while providing access to Born effective charge tensors, and infrared spectra. We benchmark student models distilled from a broad set of foundation MLIPs, including UMA, MACE, Orb, eSEN, GemNet-OC, PET, and EquiformerV2-based models, against experimental infrared spectra for liquid water, concentrated hydrochloric acid, and the anatase TiO2(101)-water interface. Across these systems, electrostatic response can be extracted from most foundation MLIPs. The benchmark further shows that the underlying DFT level and dataset used to train the teacher model play a larger role than architecture in determining electrostatic and spectroscopic accuracy. For the TiO2-water interface, fine-tuning with a modest amount of higher-level DFT data improves structural and infrared predictions. LES-based distillation therefore provides a practical route for converting foundation MLIPs into efficient, electrically responsive models, while also testing the physical fidelity encoded in foundation models.
Machine-learning force fields (MLFFs) are reliable only near their training distribution, making efficient construction of diverse training sets a major bottleneck for both train-from-scratch and foundation fine-tuning workflows. Active learning can reduce this cost, but standard model-committee uncertainty is impractical for foundation MLFFs because each committee member requires a separate fine-tuning run. We present an active-learning workflow based on last-layer-projection regression (LLPR), a forward-pass-cheap per-configuration uncertainty estimator. Across molecular, condensed-phase, and electrolyte systems, LLPR identifies compact, high-value training sets that recover full-data accuracy using only a small fraction of electronic-structure labels. In foundation-model fine-tuning, LLPR-selected configurations reach the full-pool fine-tuning ceiling with substantially fewer labels than random selection. In iterative electrolyte fine-tuning, LLPR detects unphysical local coordination before DFT labelling, provides an absolute force-error threshold, and enables automatic termination of the learning loop. The resulting models reproduce reference density and ion-coordination structure, providing a scalable uncertainty-quantification strategy across MLFF training regimes.
We introduce implicit machine learning force fields (I-MLFFs), which replace explicit stacks of neural network layers with self-consistent fixed-point equations. In molecular simulations, this formulation enables intermediate representations to be reused across successive timesteps, thereby warm-starting force evaluation. The resulting models effectively combine the computational footprint of a shallow, single-layer MLFF with the representational capacity and accuracy of a deep neural network. Our approach unlocks architecture-agnostic efficiency gains that are inaccessible when force prediction and trajectory integration are considered separately. We demonstrate this across three major classes of graph neural networks: invariant, equivariant Cartesian tensor, and SO(3)-equivariant spherical-tensor architectures. Each yields a two- to five-fold reduction in compute and memory footprint. Crucially, these gains are achieved while retaining full atomistic resolution and the original integration timestep, avoiding spatial or temporal coarse graining. Our contribution therefore advances the scaling frontier of quantum-mechanically faithful molecular simulation, enabling longer trajectories and larger atomistic systems within fixed GPU memory and compute budgets, and thereby opening access to new insights across biomolecular and material systems.