Neutron and X-ray Diffraction Reveal the Limits of Long-Range Machine Learning Potentials for Medium-Range Order in Silica Glass
Authors: Sai Harshit Balantrapu, Atul C. Thakur, Chris Benmore, Ganesh Sivaraman
Organizations: Department of Material Design and Innovation, University at Buffalo, Buffalo, NY 14260, United States of America · NVIDIA Corp., 2788 San Tomas Expressway, Santa Clara, CA 95051, United States of America · X-ray Science Division, Advanced Photon Source, Argonne National Laboratory, Lemont, IL 60439, United States of America
Glassy silica is a foundational material in optics and electronics, yet accurately predicting its medium-range order (MRO) remains a major challenge for machine-learning interatomic potentials (MLIPs). While local MLIPs reproduce the short-range SiO4 tetrahedral network well, it remains unclear whether locality alone is sufficient to recover the first sharp diffraction peak (FSDP), the principal experimental signature of MRO. Here, we combine neutron and X-ray diffraction measurements with large-scale molecular dynamics driven by two MACE-based models: a short-range (SR) potential and a long-range (LR) extension incorporating reciprocal-space gated attention. The SR model systematically over-structures the network, producing an overly intense FSDP in both the liquid and glassy states. Incorporating long-range interactions improves agreement with experiment for the liquid structure by reducing this excess ordering, but the LR model still fails to recover the experimental amorphous MRO after quenching. Ring-statistics and bond-angle analyses reveal that SR model exhibits an artificially narrow distribution dominated by six-membered rings, while the LR model produces a broader but still biased ring population. Despite preserving the correct tetrahedral geometry, both models show limited variability in Si-O-Si angles, indicating constrained network flexibility. These structural signatures demonstrate that both models retain excessive memory of the parent liquid network, leading to kinetically trapped and nonphysical medium-range configurations during vitrification. These results show that explicit long-range interactions are necessary but not sufficient for predictive modelling of disordered silica and suggest that accurate MRO further requires training data and sampling strategies that adequately represent the liquid-to-glass transition.
First-principles atomistic simulations are essential for understanding complex material phenomena but are fundamentally limited by their computational cost. While Machine Learning Interatomic Potentials (MLIPs) have drastically improved cost for a given accuracy, their inference cost remains a bottleneck for massive systems or long timescales. To address this, we introduce a multifidelity "Mixture-of-Experts" framework based on the E(3)-equivariant Allegro architecture. Our method spatially partitions the simulation domain into a chemically complex region (e.g., reactive interfaces) and a simple region (e.g., bulk lattice), assigning models of varying capacity to each. Among the challenges in such static domain decomposition, the mechanical mismatch between models at the interface is particularly critical, as it can generate artificial stress fields and instability. We address this challenge with a co-training strategy in which the loss function includes agreement constraints -- penalties on per-atom energy and force discrepancies between models evaluated on shared bulk environments -- forcing the independent models to learn a consistent physical description of the bulk material. We validate this approach on a realistic Pt+CO catalytic system, demonstrating that the co-trained models maintain exact energy conservation, align their bulk mechanical response (e.g., equation of state and bulk modulus), and achieve predictive accuracy comparable to a full high-fidelity simulation at more than twice the computational speed.
Gabriel de Miranda Nascimento, Marc L. Descoteaux, Laura Zichi +9
Long-range electrostatics and polarization remain central obstacles to extending machine learning interatomic potentials (MLIPs) to ionic, polar, and interfacial systems. Here we introduce a semi-local framework for learning electrostatics from energies and forces using polarizable atomic multipoles. Local equivariant descriptors predict environment-dependent latent monopoles, dipoles, and quadrupoles, while residual non-local charge transfer and polarization are captured by non-self-consistent linear response in induced charges and dipoles. Across four diverse benchmarks and four short-range MLIP architectures, the multipole hierarchy and response terms systematically improve potential energy surface accuracy, with the largest gains in systems where long-range effects are essential. More importantly, physically meaningful electrical responses emerge without direct supervision. The learned latent multipoles yield accurate Born effective charge tensors and infrared spectra in close agreement with experiments. The induced-dipole extension introduces new capabilities: it predicts polarizabilities and thereby enables semi-quantitative Raman spectra for bulk water and hybrid MAPbI3 perovskite, as well as the essential features of the surface-specific vibrational sum-frequency generation spectrum at the water-air interface. In ferroelectric HfO2, the predicted electrical response also captures LO-TO splitting and polarization switching. This systematically improvable, physically transparent framework enables MLIPs trained on standard energy and force labels to predict polarization-sensitive observables.
Realistic physical systems are characterised by emergent interactions across multiple length and time scales, posing a significant challenge for predictive machine learning (ML) models. Most scientific ML models focus on a narrow range of interactions. While machine learning force fields (MLFFs) offer near-quantum accuracy, the ubiquitous message-passing layers miss long-range many-body effects. Here we introduce the Multiscale Structural Ensemble (MuSE), a hierarchical model that uses Soft Coarse-Graining Pooling to construct coarse representations from smooth fractional assignments of atoms to coarse nodes, enabling MLFF modules to operate across multiple scales. MuSE is architecture-agnostic and coupled with SO3krates, MACE, and PaiNN MLFFs for both molecules and materials. We demonstrate the power of MuSE through Hessian-based benchmarks, folding trajectories for biomolecules, and energy profiles in molecule-graphene nanostructures, where MuSE accurately captures quantum-mechanical interactions at relevant scales -- unlike other recent long-range ML models.
Àlex Solé, Sergio Suárez-Dou, Albert Mosella-Montoro +4