Anisotropic representations for E(3)-equivariant machine learning coarse-grained potentials

Rem3Di: Learning smooth, chiral 3D molecular descriptors from atomistic foundation models

Rem3Di is introduced, a representation-learning framework that repurposes latent features from atomistic foundation models as transferable molecular descriptors for property prediction and virtual screening and provides a route from simulation-trained atomistic representations to transferable, chirality-aware molecular representations for chemical machine learning.

Reconstructing local environments from concise atomistic representations

Symmetry-based representations of local atomic structure, such as the power spectrum or bispectrum, are routinely used to characterize the structural diversity of datasets and as input features for atomistic machine learning. Although these descriptors systematically incorporate increasingly complex geometric correlations, it remains unclear if a given feature can be mapped back to a discrete point cloud, whether such a reconstruction is unique, and how changes in the descriptor are reflected in the underlying atomic geometry. The choice and discretization of the radial and angular bases, as well as the high dimensionality of the resulting feature vectors -- which may contain hundreds or thousands of components -- make this interpretation even more challenging. In this work, we investigate the inverse problem of recovering atomic structures from local invariant descriptors. We show that accurate reconstructions can be obtained from remarkably compact descriptors of different correlation orders, each comprising only a few tens of features. Even representations that are formally incomplete or locally ill-conditioned can be inverted to accurate geometric reconstructions of atomic environments across molecular and material datasets. Our reconstruction framework provides a general algorithmic means of identifying approximate degeneracies of invariant descriptors and recovering distinct atomic environments that cannot be distinguished by a given representation. Finally, by reconstructing atomic configurations from descriptors, we examine how perturbations in invariant descriptors of different correlation orders translate into structural distortions.

A geometric rotation-equivariant spherical convolutional and gaussian radial basis network for predicting protein-ligand binding affinity

STEP: Spin Tensor Equivariant Potential for Data-Efficient Learning of Magnetic Potential Energy Surfaces

Accurate and efficient modeling of magnetic potential energy surfaces remains challenging because spin-polarized first-principles calculations for diverse non-collinear spin-lattice configurations are computationally demanding. Here we introduce the Spin Tensor Equivariant Potential (STEP), a magnetic machine-learning interatomic potential that treats vector magnetic moments as continuous geometric degrees of freedom and embeds them in an equivariant representation. By coupling the central spin representation to its local spin-lattice environment through a Center-Environment Tensor Product, STEP introduces a physics-informed bias while preserving translational invariance and $\mathrm{SO}(3)$ equivariance and supporting feature-level time-reversal symmetrization. Learning-curve analysis on monolayer CrI$_3$ shows that STEP achieves pronounced data efficiency, with higher-order tensor channels and iterative center-environment couplings leading to steep learning curves for energy, force, and magnetic force errors. On public FeAl, CrN, and Fe benchmarks, STEP achieves competitive or improved accuracy compared with recent magnetic machine-learning potentials. Using a compact but representative CrI$_3$ dataset, STEP reproduces phonon dispersions and magnon spectra with high fidelity, capturing subtle anisotropic magnetic interactions. For Fe$_2$Mo$_3$O$_8$, STEP further provides a quantitative description of magnon--phonon hybridization and reproduces its characteristic magnon polaron dispersion. Finally, spin dynamics simulations driven by STEP yield Curie temperatures for monolayer CrI$_3$ and bcc Fe in good agreement with experiments. These results establish STEP as a physically informed, data-efficient, and scalable framework for modeling spin-lattice coupling, magnetic excitations, and finite-temperature magnetic behavior.

Machine learning of electronic structure and atomistic properties from the external potential.

This work proposes an operator-centric framework in which the external (nuclear) potential, expressed in an AO basis, serves as the model input and builds hierarchical, body-ordered representations of atomic configurations that closely mirror the principles underlying several popular atom-centered descriptors.

Implicit Machine Learning Force Fields Accelerate Molecular Dynamics Simulations

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.