Smooth Dynamic Cutoffs for Machine Learning Interatomic Potentials

TL;DR

This work introduces a smooth dynamic cutoff for MLIPs that per-atomizes the neighborhood radius to target a desired average neighbor count $\mu$ within a hard cutoff $h$, thereby inducing graph sparsity while preserving the second-order differentiability required for stable molecular dynamics. The authors formulate a ranking-based neighbor selection with a Gaussian weight and a stable, differentiable cutoff $c_v$, and demonstrate stability across long MD runs. Implemented on four state-of-the-art models (MACE, Nequip, OrbV3, TensorNet) and evaluated on molecular (MD22) and materials (MatPES) datasets, the approach achieves up to $2.26\times$ memory savings and $2.04\times$ faster inference with only minor accuracy degradation. The method robustly handles density changes, offers clearer stability advantages over reducing fixed cutoffs, and can be combined with other acceleration strategies for even larger-scale simulations; all code is open-sourced. This scalable, differentiable sparsification enables MLIP-driven MD to tackle substantially larger systems in practical timeframes.

Abstract

Machine learning interatomic potentials (MLIPs) have proven to be wildly useful for molecular dynamics simulations, powering countless drug and materials discovery applications. However, MLIPs face two primary bottlenecks preventing them from reaching realistic simulation scales: inference time and memory consumption. In this work, we address both issues by challenging the long-held belief that the cutoff radius for the MLIP must be held to a fixed, constant value. For the first time, we introduce a dynamic cutoff formulation that still leads to stable, long timescale molecular dynamics simulation. In introducing the dynamic cutoff, we are able to induce sparsity onto the underlying atom graph by targeting a specific number of neighbors per atom, significantly reducing both memory consumption and inference time. We show the effectiveness of a dynamic cutoff by implementing it onto 4 state of the art MLIPs: MACE, Nequip, Orbv3, and TensorNet, leading to 2.26x less memory consumption and 2.04x faster inference time, depending on the model and atomic system. We also perform an extensive error analysis and find that the dynamic cutoff models exhibit minimal accuracy dropoff compared to their fixed cutoff counterparts on both materials and molecular datasets. All model implementations and training code will be fully open sourced.

Figures (11)

• Figure 1: We introduce a dynamic cutoff function which induces graph sparsity onto the underlying atom graph while maintaining simulation stability. The dynamic cutoff function calculates a dynamic radius that targets a specific number of atoms to be within the dynamic radius while pruning the rest. This sparsification method leads to up to 2.26x reduction in memory consumption and up to 2.04x reduction in inference time depending on the model and atomic system.
• Figure 2: The potential energy surface (PES) of a fixed cutoff, max neighbors, and dynamic cutoff TensorNet model on a random system. The fixed cutoff baseline and dynamic cutoff energy surfaces exhibit smooth characteristics while the energy surface resulting from setting a strict maximum neighbor is highly jagged and unsmooth. The PES associated with the maximum neighbor model leads to highly unstable and un-usable molecular dynamics simulation while the the fixed cutoff and dynamic cutoff models lead to stable simulation.
• Figure 3: Plots showing the total energy drift in meV/atom of a 100 ps NVE molecular dynamics simulation using the dynamic cutoff models. DWNT refers to the double walled nanotube system from the MD22 dataset. LiFePO4 refers to an LiFePO4 supercell simulated at 3000K in order to stress test the dynamic cutoff by inducing a large number of neighbor switches throughout the simulation. Besides standard perturbations within the energy due to numerical integration, there exists no systemic drift throughout the entirety of the simulation.
• Figure 4: (a) A plot of the memory reduction (higher is beter) of the MACE, Nequip, Orbv3, and TensorNet models when using a dynamic cutoff compared to a fixed cutoff for a periodic material (MOF) and biomolecular protein system. The target number of neighbors, $\mu$ is 40 and 20 for the material and molecular systems respectively. (b) A plot of the inference time speedup (higher is better) for each of the 4 models on the two systems relative to the fixed cutoff inference time.
• Figure 5: The relative force MAE increase of the dynamic cutoff TensorNet model trained on the MatPES dataset compared its fixed cutoff counterpart. The relative error increase is plotted with respect to the Clementi calculated atomic radius.

Theorems & Definitions (4)

• Theorem 3.1
• proof
• Theorem 1.1
• proof