Enabling Structure-Only Initialization and Out-of-Distribution Generalization in GNN-based Molecular Dynamics Simulators

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.

Amorphous materials exhibit exceptional mechanical and functional properties, yet their rugged energy landscapes are notoriously difficult to sample. Below the glass-transition temperature, conventional molecular dynamics and Monte Carlo become inefficient because equilibration relies on rare barrier-crossing events, while data-driven generative models are constrained by scarce and biased reference ensembles. Here, we introduce ATLAS, an efficient sampler that learns a diffusion process to generate Boltzmann-distributed amorphous structures directly from a target energy function. Parameterized by an equivariant graph neural network, ATLAS generalizes across system size, temperature, and composition. By exploiting the time reversal of the diffusion process, it enables efficient estimation of thermodynamic quantities and steering toward target observables. In two-dimensional Kob-Andersen systems, ATLAS reproduces parallel tempering Markov chain Monte Carlo structural distributions, free energies and entropies, achieving below 0.2% free energy error in the low-temperature glass regime with over 500-fold fewer energy evaluations. In Cu-Zr and Cr-Co-Ni metallic glasses, ATLAS recovers experimentally observed short-range-order trends and steers structures toward prescribed order parameters and optimized bulk moduli. Moreover, composition-amortized pretraining outperforms composition-specific training from scratch, reduces inverse-design costs by several hundred-fold, and enables sampling with expensive universal machine learning interatomic potentials. Coupled to a large language model agent, ATLAS searches an eight-element space for high-entropy metallic glasses balancing stiffness and ductility, identifying a converged Pareto frontier within 480 oracle evaluations. Together, these results establish ATLAS as a foundation model for sampling, steering and designing amorphous materials.

Machine-learning drug-discovery pipelines increasingly rely on generative models that propose molecules far from the data used to train downstream synthesizability filters. Existing filters (SAScore, SCScore, RAscore, DeepSA) are purely statistical and degrade in exactly this out-of-distribution (OOD) regime. We ask whether cheap, closed-form physical priors, used as auxiliary supervision on a graph neural network (GNN), improve OOD generalization. We add two auxiliary losses to a GINE backbone: a topological complexity regression supervised by the Bertz index, and a strain-energy soft penalty supervised by MMFF94 force-field energy. On a 65,177-molecule corpus (HIV, Tox21, COCONUT) labeled by SAScore thresholds we reproduce a strong in-distribution baseline, then evaluate a 4-way ablation (baseline / +complexity / +strain / +both) on a single-source OOD split (train on drug-like HIV+Tox21, test on COCONUT natural products), repeated over 5 seeds with paired bootstrap confidence intervals. All three physics-aware variants give a small but statistically significant OOD improvement over the baseline (mean OOD AUC 0.9774): +complexity Delta = +0.0060 (95% CI [+0.0023, +0.0102]), +strain Delta = +0.0032 ([+0.0008, +0.0052]), +both Delta = +0.0066 ([+0.0038, +0.0093]); every interval excludes zero, and the combination is best. The variants are indistinguishable in-distribution, so the effect is visible only under OOD evaluation. We are explicit that the effects are modest, and we report a cautionary methodological finding: a single-seed version of this experiment produced a qualitatively different (non-monotone) story that did not survive multi-seed evaluation.