🤖 machine learning

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

The paper introduces EquiFiLM, a lightweight, E(3)-equivariant extension that enables foundation machine learning force fields to accurately model charge-conditioned potential energy surfaces and driven processes with minimal training data by integrating Feature-wise Linear Modulation blocks.

Original authors: Samuel Sahel-Schackis, Ken-ichi Nomura, Aiichiro Nakano, Matthias F. Kling, Thomas Linker

Published 2026-07-08

📖 4 min read☕ Coffee break read

CC BY 4.0

Original authors: Samuel Sahel-Schackis, Ken-ichi Nomura, Aiichiro Nakano, Matthias F. Kling, Thomas Linker

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you have a super-smart, highly trained chef (let's call him "Chef MACE") who can cook the perfect meal for a standard, neutral dinner party. He knows exactly how to arrange the ingredients (atoms) to make a delicious, stable dish (a molecule). He's so good that his cooking is almost as perfect as a Michelin-starred chef who calculates every chemical reaction from scratch.

However, there's a problem: Chef MACE only knows how to cook for a neutral dinner. If you suddenly tell him, "Hey, this party has a huge electrical charge now!" or "The room is super hot!" or "We need to simulate a high-pressure environment," he freezes. He doesn't know how to change his recipe. He keeps cooking the exact same neutral meal, even though the conditions have changed. In the real world of chemistry, changing the charge or temperature completely changes how atoms behave, and Chef MACE's old recipes would lead to a culinary disaster (unstable simulations).

Enter EquiFiLM: The "Seasoning Adapter"

The authors of this paper invented a tiny, lightweight add-on called EquiFiLM. Think of it not as a new chef, but as a smart seasoning shaker that you clip onto Chef MACE's apron.

Here is how it works in simple terms:

The Problem with Old Solutions:
- Option A (The "One Chef Per Charge" method): You could hire a different chef for every single type of party (one for neutral, one for +1 charge, one for +2 charge, etc.). This is expensive and requires hiring thousands of chefs (training massive amounts of data).
- Option B (The "Rebuild from Scratch" method): You could try to teach Chef MACE how to handle charges by making him relearn everything from the ground up. This requires an impossible amount of practice data (billions of examples).
The EquiFiLM Solution:
- Instead of firing Chef MACE, you just clip this smart seasoning shaker onto him.
- This shaker has a dial. When you turn the dial to "Charge: +10," the shaker instantly whispers a specific set of instructions to Chef MACE: "Okay, for this charge, tweak the saltiness of the first layer of ingredients, adjust the spice in the second layer, but leave the main structure alone."
- The Magic Trick: The shaker only tweaks the "scalar" parts of the recipe (the basic numbers like salt and sugar). It leaves the complex "shape" of the dish (the geometry and 3D structure) exactly as Chef MACE knows it. This ensures the dish still looks and behaves correctly in 3D space, no matter how you season it.

What Did They Test?

They tested this on charged liquid water. Imagine a glass of water where they added a massive electrical charge to it.

Without the shaker: The simulation fell apart. The forces (the "push and pull" between atoms) were wrong by a huge margin, like trying to build a house with a hammer instead of a screwdriver.
With the EquiFiLM shaker: The model became incredibly accurate. It predicted how the water atoms would move and arrange themselves under different charges with near-perfect precision.

Key Takeaways from the Paper:

It's a "Plug-and-Play" Upgrade: You don't need to rebuild the whole kitchen. You can take any existing, high-quality "foundation" model (like MACE-MatPES) and clip this adapter on top.
It's Data Efficient: To teach a brand-new chef how to handle charges, you'd need millions of practice meals. To teach Chef MACE with the shaker, they only needed about 6,400 examples. That's a massive saving.
It's Fast: Adding this shaker didn't slow down the cooking process at all. It runs just as fast as the original chef.
It Generalizes: They trained the shaker on charges of 0, 6, 10, and 16. Then, they asked it to handle charges of 2, 8, 14, and even 20 (which it had never seen before). It handled them smoothly, like a chef who understands the concept of seasoning rather than just memorizing recipes.
It Predicts Real Physics: The model didn't just guess numbers; it successfully simulated how the water structure changes (like the distance between oxygen atoms) when charged, matching what ultrafast electron diffraction experiments would see.

The Bottom Line

The paper claims that EquiFiLM is a clever, lightweight way to give existing, powerful AI chemistry models the ability to handle external changes (like electrical charge) without needing to retrain them from scratch. It turns a rigid, "one-size-fits-all" model into a flexible one that can adapt to different conditions just by turning a dial, saving massive amounts of time and computing power.

Note: The paper specifically demonstrates this with electrical charge on liquid water. While the authors suggest the method could theoretically work for temperature or pressure, the paper's actual results and claims are strictly limited to the charge-conditioning of water molecules.

Technical Summary: EquiFiLM

Problem Statement

Foundation machine-learning force fields (MLFFs), such as MACE-MP-0 and UMA, have achieved near-density functional theory (DFT) accuracy across broad chemical spaces. However, standard formulations condition exclusively on atomic positions and species, assuming equilibrium ground-state physics. They lack a native mechanism to handle externally induced changes to the electronic state, such as total charge, applied fields, or electronic excitation. Consequently, these models fail to generalize to driven processes like photoexcitation or charge injection.

Existing approaches to incorporate external conditioning face significant trade-offs:

Per-state specialists: Training separate models for each charge state yields acceptable accuracy for the training charge but fails to generalize to unseen charges.
Physics-grounded foundations: Models like MACE-POLAR-1-M or 4G-HDNNP are built with explicit charge-awareness (e.g., charge equilibration, per-atom Coulomb machinery). While effective, they require training from scratch on massive corpora (order of $10^8$ structures) and often involve complex, dedicated atomic-charge supervision or iterative equilibration.
Degradation: Applying a standard foundation model to charged systems results in rapid accuracy degradation, with force errors rising into hundreds of meV/Å.

Methodology

The authors propose EquiFiLM, a lightweight, backbone-agnostic adapter that adds a continuous external conditioning axis to any equivariant foundation MLFF.

Core Mechanism: ChargeFiLMBlock

The method utilizes Feature-wise Linear Modulation (FiLM), adapted specifically for equivariant networks.

Input: A per-graph conditioning scalar $c$ (e.g., total charge $q$ normalized by atom count).
Architecture: Two small Multi-Layer Perceptrons (MLPs) map $c$ to gating parameters $\gamma(c)$ and $\beta(c)$ .
Modulation: The block is inserted between the message tensor and the linear projection in every interaction layer of the backbone. It modulates only the scalar channels ( $\ell=0$ ) of the node features:
$m'^{(t, \ell=0)}_i = (1 + \gamma(c)) \odot m^{(t, \ell=0)}_i + \beta(c)$
Higher-order equivariant features ( $\ell \ge 1$ ) pass through unchanged.
Equivariance Preservation: Since the gating parameters depend only on a per-graph scalar (which is invariant under rotation and translation) and the modulation acts solely on scalar channels, the block preserves E(3)-equivariance exactly.
Initialization: The output layers of the gating MLPs are initialized to zero, ensuring that at the start of training, the adapter acts as an identity function, making the model bit-identical to the unconditioned backbone.

Implementation Details

Backbone: The method is demonstrated using MACE-MatPES as the backbone.
Training Data: The model is trained on ab initio molecular dynamics (AIMD) trajectories of liquid water at four total charges ( $q \in \{0, 6e, 10e, 16e\}$ ) using VASP at the r2SCAN meta-GGA level.
Efficiency: The adapter adds approximately 15% parameters relative to the backbone but incurs no measurable per-step inference cost compared to the unconditioned backbone.

Key Results

The resulting model, E-MACE, was evaluated on charged liquid water across training, interpolation, and extrapolation charges.

Accuracy and Generalization

Training Charges: E-MACE achieves a 3.1× reduction in force RMSE (21.3 to 6.96 meV/Å) and a 61× reduction in per-atom energy RMSE (6.1 to 0.1 meV/atom) compared to a baseline MACE-MatPES fine-tuned on the same data without EquiFiLM.
Comparison to Large Foundations: E-MACE matches the force accuracy of MACE-POLAR-1-M, a purpose-built charge-aware foundation that is ~20× larger (15.2M vs. 0.76M parameters) and trained from scratch on massive datasets.
Generalization: The model generalizes to held-out interpolation ( $q \in \{2e, 4e, 8e, 12e, 14e\}$ ) and extrapolation ( $q \in \{18e, 20e\}$ ) charges. Force RMSE remains within 18–61 meV/Å, and energy RMSE within 0.7–5.4 meV/atom.
Data Efficiency: High accuracy is achieved with minimal data. Energy RMSE saturates with just 25% of the training data (~~1,600 frames), and force RMSE saturates at 50% (~~3,200 frames). This contrasts with the $\approx 10^8$ structures required for training charge-aware foundations from scratch.

Physical Consistency

Energy Conservation: Molecular dynamics (MD) simulations using E-MACE demonstrate stable energy conservation in the microcanonical (NVE) ensemble across the full charge range, with mean drifts below 0.01 meV/atom. This confirms that the FiLM block preserves the conservative nature of the forces.
Structural Response: The model successfully predicts the charge-dependent response of the reduced pair distribution function (PDF), $\Delta G(r; q)$ . It captures the outward shift of the first O-O coordination shell and the emergence of H-H peaks at high charges (indicating reductive H $_2$ formation), consistent with ultrafast electron diffraction (UED) observables.

Ablation Studies

Modulation Type: The additive shift $\beta$ alone captures most of the performance gain, suggesting the primary effect of charging is a baseline energy shift. The multiplicative gate $\gamma$ is retained for generality (e.g., for temperature/pressure scaling) and adds negligible cost.
Input Injection: Simply concatenating charge as an input token (without per-layer modulation) fails to improve accuracy, confirming that per-layer modulation is necessary for the network to adjust internal features at every depth.

Significance and Claims

The paper claims that EquiFiLM establishes a new paradigm for extending foundation MLFFs to driven processes:

Adapter Problem: Conditioning a foundation MLFF is framed as an "adapter problem," analogous to task adaptation in language and vision. It requires only a small fine-tuning corpus (thousands of frames) spanning the conditioning axis, rather than retraining the foundation from scratch.
Backbone and Conditioning Agnostic: The recipe applies without architectural changes to any equivariant MLFF with scalar interaction-layer channels and can handle any continuous scalar external variable (e.g., charge, temperature, pressure, doping fraction).
Efficiency vs. Performance: It achieves accuracy comparable to massive, purpose-built charge-aware foundations at a fraction of the parameter count and training data cost, while maintaining the inference speed of the original backbone.
Physical Validity: By strictly preserving E(3)-equivariance and acting only on scalar channels, the method ensures that the resulting forces remain exact gradients of a position-dependent energy, enabling stable, long-timescale MD simulations.

The authors conclude that this approach makes it feasible to add controllable degrees of freedom (like charge or temperature) to existing foundation models for applications in electrochemistry, photochemistry, and doped-materials design without the prohibitive cost of training new foundations.