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PyTorch framework for training neural network interatomic potentials with the Equivariant Transformer (ET) architecture and its efficient TensorNet successor, providing equivariant message passing with linear complexity in tensor order; underpins the MACE-OFF and SPICE models and widely adopted across molecular dynamics and materials simulation workflows (Amsterdam Machine Learning Lab / De Fabritiis Group, 483+ stars, MIT License, actively maintained)

E(3)-equivariant neural network interatomic potentials achieving DFT accuracy with up to 1000× less training data than invariant models, foundational architecture behind MACE and Allegro (Harvard, MIT, Nature Communications 2022)

Diffusion-based generative model for inorganic materials design, steering generation by chemistry, symmetry, bulk modulus, band gap, or magnetic properties, 2× more likely to produce stable novel structures than prior methods, experimentally validated with synthesized TaCr₂O₆ (Microsoft, Nature 2025)

Neural network-based exchange-correlation functional for density functional theory (DFT) that surpasses state-of-the-art hybrid functionals in accuracy for main-group thermochemistry, kinetics, and non-covalent interactions at semi-local DFT cost; includes PySCF/GPU4PySCF/ASE bindings and C++/Fortran integrations (248+ stars, MIT License)

Deep learning atomistic model across elements, temperatures, and pressures

Graph neural network interatomic potential package supporting efficient multi-GPU parallel molecular dynamics simulations, enabling large-scale atomistic modeling with machine learning potentials (MDIL-SNU, MIT License)

Family of large language models for materials research via continued pretraining of LLaMA-2/3 on ~30B materials science tokens, outperforming commercial LLMs on materials science tasks while identifying "adaptation rigidity" in overtrained models; includes MatNLP benchmark and CIF crystal generation capabilities (IIT Delhi M3RG, MIT License)

Highly scalable equivariant deep learning interatomic potentials enabling million-atom molecular dynamics simulations with ab initio accuracy, building on E(3)-equivariant architectures for large-scale atomistic modeling (mir-group, MIT License, 480+ stars)

Equivariant foundation models for materials "on a budget", releasing pre-trained universal interatomic potentials (nequix-mp-1 on MPtrj, nequix-omat-1 on OMat24, nequix-oam-1 combining OMat24, sAlex, and MPtrj frontier datasets) with phonon fine-tuning (PFT) for accurate lattice dynamics and analytical Hessians; pip-installable with ASE calculator and JAX/PyTorch backends with OpenEquivariance kernels (Atomic Architects, 76+ stars, MIT License, 2025-2026)

Materials informatics benchmark

Crystal property prediction