Learning consistent molecular mechanics force fields from first principles

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.

Machine-learned interatomic potentials (MLIPs) excel at in-distribution tasks, accelerating drug and material development, yet they struggle to generalize out-of-distribution. We propose to push the cost-accuracy Pareto frontier by designing observable-agnostic electronic ground-state descriptor models (GSMs) with computational costs situated between MLIPs and Kohn-Sham density functional theory (KS-DFT). We align the learning objectives and architectures of GSMs with the governing equations of KS-DFT by enforcing physical constraints and removing optimization pressure on unphysical or irrelevant degrees of freedom. In our size-extrapolation experiments from QM9 to QM40, our combined contributions OrthoNormal-Loss (ON-Loss) and Grassmann Restricted Occupied-Orbital Training (GROOT) reach a 79.1% energy and 83.4% force mean absolute error (MAE) reduction over previous state-of-the-art density GSMs. For Hamiltonian GSMs, ON-Loss and Residual Optimal-gauge Conditioning-aware KS-Eq. Training (ROCKET) together reduce the energy and force MAEs of the strongest baseline by 99.8% and 95.9%, respectively. Using a self-consistency rejection criterion, we filter out extrapolation errors on QMugs, rejecting fewer than 0.4% of predictions while reaching an energy MAE of 0.07 mHa. Finally, we demonstrate the efficiency of label-free self-consistency fine-tuning, and transfer GSMs to reactive chemistry in Transition1x, reaching energy errors below chemical accuracy.

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.