GFFMERGE: Efficient Merging of Graph Neural Force Fields and Beyond

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.

Point defects play a central role in driving the properties of materials. First-principles methods are widely used to compute defect energetics and structures, including at scale for high-throughput defect databases. However, these methods are computationally expensive, making machine-learning force fields (MLFFs) an attractive alternative for accelerating structural relaxations. Most existing MLFFs are based on graph neural networks (GNNs), which can suffer from oversmoothing, oversquashing, and poor representation of long-range interactions. Both of these issues are especially of concern when modeling point defects. To address these challenges, we introduce the \textit{Accelerated Deep Atomic Potential Transformer} (ADAPT), an MLFF that replaces graph representations with a direct coordinates-in-space formulation and explicitly considers all pairwise atomic interactions. Atoms are treated as tokens, with a Transformer encoder modeling their interactions. Applied to a dataset of silicon point defects, ADAPT achieves a roughly 22% reduction in force and a roughly 40 percent reduction in energy prediction error relative to a state-of-the-art GNN-based model, while requiring only a fraction of the computational cost.

Molecular message-passing neural networks commonly propagate chemically diverse interactions through a single graph, which may mix interaction-specific signals and require deep propagation to capture long-range effects. We introduce the Multi-level, Multi-color Graph Neural Network (MMGNN), a hierarchical framework that decomposes a molecular graph into overlapping atom-type-pair-specific subgraphs while preserving atom-level resolution. MMGNN-2D constructs chemical-colored subgraphs from covalent connectivity, whereas MMGNN-3D constructs geometric-colored subgraphs from spatial proximity and augments their edges with distance, angular, and torsional descriptors. Both variants apply a shared communicative message-passing backbone to each subgraph and combine the resulting representations through atom-wise aggregation and molecular readout. We evaluated MMGNN on five classification and three regression benchmarks from MoleculeNet using common scaffold splits and five independent runs. MMGNN-2D achieved the highest macro-average AUC-ROC of 0.838 across the classification datasets and the lowest RMSE on ESOL (0.803). MMGNN-3D obtained the highest mean AUC-ROC on BBBP (0.956) and the lowest RMSE on FreeSolv (1.793), indicating complementary strengths of topological and geometric representations. Structural and leave-one-out analyses further illustrate how the subgraph decomposition affects learned representations and atom-type-pair sensitivities. These results support overlapping interaction-specific graph decomposition as a competitive strategy for molecular property prediction.