Scalable Machine Learning Force Fields for Macromolecular Systems Through Long-Range Aware Message Passing

TL;DR

The paper addresses the limitation of fixed-cutoff local ML force fields in adequately modeling long-range interactions in macromolecular systems. It introduces MolLR25, a benchmark suite up to 1200 atoms with high-fidelity DFT labels, and proposes E2Former-LSR, a SO(3)-equivariant transformer that explicitly integrates long-range attention via a Long–Short Range (LSR) message passing framework and chemically informed fragmentation. E2Former-LSR demonstrates stable, near-constant force error scaling beyond 1200 atoms, captures non-covalent decay more accurately, and achieves up to 30% speedup over purely local models, validated across long-range dissociation, medium-scale protein conformations, and large-MD trajectories. The results underscore that non-local architectural design is essential for generalizable ML force fields, enabling high-fidelity molecular dynamics for large biological and chemical systems.

Abstract

Machine learning force fields (MLFFs) have revolutionized molecular simulations by providing quantum mechanical accuracy at the speed of molecular mechanical computations. However, a fundamental reliance of these models on fixed-cutoff architectures limits their applicability to macromolecular systems where long-range interactions dominate. We demonstrate that this locality constraint causes force prediction errors to scale monotonically with system size, revealing a critical architectural bottleneck. To overcome this, we establish the systematically designed MolLR25 ({Mol}ecules with {L}ong-{R}ange effect) benchmark up to 1200 atoms, generated using high-fidelity DFT, and introduce E2Former-LSR, an equivariant transformer that explicitly integrates long-range attention blocks. E2Former-LSR exhibits stable error scaling, achieves superior fidelity in capturing non-covalent decay, and maintains precision on complex protein conformations. Crucially, its efficient design provides up to 30% speedup compared to purely local models. This work validates the necessity of non-local architectures for generalizable MLFFs, enabling high-fidelity molecular dynamics for large-scale chemical and biological systems.

Figures (4)

• Figure 1: Architectural necessity and benchmark scope for long-range MLFFs. a. Distribution of system size ($\mathcal{N}$) and maximum inter-atomic distance ($R_{\text{max}}$) for common benchmark datasets (QM9, MD17, MD22, OMol25) compared to the proposed $\emph{MolLR25}$ suite. The ${MolLR25}$ data extends significantly beyond existing benchmarks, covering systems up to $\mathcal{N} \approx 1200$ atoms and spatial ranges up to $R_{\text{max}} \approx 75\text{\r{A}}$. b. Scaling behavior of the training error ($\text{RMSE}_{\text{train}}$) versus system size ($\mathcal{N}$) for the local $\text{MACE-large}$ model and the non-local $\text{E2Former-LSR}$. $\text{E2Former-LSR}$ exhibits a notably flatter and converging error curve as complexity increases, demonstrating its robust capacity to integrate long-range dependencies. c. Schematic of the $\text{E2Former-LSR}$ architecture. The design overcomes the fixed-cutoff limit by segmenting the molecule into fragments and utilizing a transformer-based attention mechanism to jointly model short-range atom-atom interactions and long-range atom-fragment interactions for comprehensive feature aggregation.
• Figure 2: Evaluation of long-range force and energy prediction accuracy on the Di-Molecule Dissociation dataset.a. Distance-resolved evaluation of MAEs for energy and force, together with CS$_f$. E2Former-LSR achieves smoother decay and higher directional consistency across all distances, especially in the transition region between short-range repulsion and long-range interaction. b. Spatial visualization of force error magnitude for representative molecular dimers at three separation distances (1$\text{\r{A}}$, 4$\text{\r{A}}$, and 8$\text{\r{A}}$). Compared with MACE, E2Former-LSR maintains substantially lower and more uniformly distributed errors as molecular interaction decreases. c. Single-system dissociation trajectory demonstrating prediction smoothness and physical continuity. The model outputs are evaluated across 100 frames with separation distances ranging from 0.2$\text{\r{A}}$ to 10$\text{\r{A}}$ in 0.1$\text{\r{A}}$ increments. E2Former-LSR accurately captures the asymptotic decay of forces and preserves a continuous and smooth potential energy surface, while MACE exhibits discontinuities and elevated errors at intermediate ranges.
• Figure 3: Evaluation of model accuracy on large biomolecular systems in the Medium-Scale Protein Conformation Fidelity benchmark. Four representative protein systems (BBL, Homeodomain, $\alpha$3D, and $\lambda$-repressor) extracted were used to assess robustness under realistic conformational complexity. a. Atom-wise force error visualizations reveal that while MACE predictions exhibit spatially localized and context-dependent errors, E2Former-LSR produces substantially smoother and consistently lower-magnitude error distributions across all structures, reflecting its capacity for accurate non-local reasoning. b. Force-resolved analysis of mean absolute error as a function of true force magnitude. MACE demonstrates increased error variance sensitive to high-force intensity, whereas E2Former-LSR maintains uniformly low and stable error across the entire force spectrum. Corresponding energy error trends show that E2Former-LSR consistently preserves accuracy across high-dimensional conformational states, unlike MACE, which exhibits increased error sensitivity in higher energy regimes.
• Figure 4: Validation of long-term dynamic stability and structural fidelity of E2Former-LSR and MACE.a. Interatomic atomic distance distribution derived from MD trajectories generated by E2Former-LSR and MACE, benchmarked against ab initio MD (AIMD) references across seven representative large-molecule systems. These systems include pure water clusters, solvated inorganic salts ($\text{NaCl}$, $\text{NaOH}$, and $\text{H}_2\text{SO}_4$), solvated organic molecules (Gln-Gly and sucrose), and the $\text{ZIF-8}$ Metal-Organic Framework. The probability density presented are tailored to specific structural features (e.g., $\text{Cl-O}$, $\text{S-O}$, $\text{Zn-N}$) to reflect local ordering. Both MLFFs accurately capture the first coordination shell (first peak), but E2Former-LSR maintains a consistently tighter agreement with the AIMD reference, particularly across the medium-range correlations ($4\text{\r{A}}$ to $6\text{\r{A}}$). b. Power spectrum computed from the velocity autocorrelation functions for the solvated $\text{NaCl}$ cluster and the $\text{ZIF-8}$ framework. E2Former-LSR accurately reproduces the full vibrational spectrum, faithfully aligning the peak positions (representing collective modes) and spectral shapes with the AIMD reference. These results confirm that the superior force fidelity of E2Former-LSR directly translates to stable, high-accuracy structural and dynamic properties in extended MD simulations.