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A curated directory of machine-learning interatomic potentials (MLIPs). Each entry lists the model name, category, release year, authoring group, and a short description.
Category: Equivariant · Year: · Authors: Harvard (Kozinsky) / MIT (Smidt)
E(3)-equivariant message-passing potential that set the template for data-efficient, high-accuracy force fields across molecules and materials.
License: MIT
Tags: equivariant, message-passing, E(3)
Category: Equivariant · Year: · Authors: Harvard (Kozinsky lab)
Strictly local equivariant architecture designed for massive parallel MD (100M+ atoms) while retaining NequIP-level accuracy.
License: MIT
Tags: equivariant, strictly local, parallel MD
Category: Transformer · Year: · Authors: Meta FAIR / MIT (Liao, Smidt et al.)
Improved equivariant transformer with higher-degree tensor representations; achieves state-of-the-art OC20/OC22 performance with strong data-efficiency.
License: MIT
Tags: transformer, equivariant, attention, higher-order tensors
Category: Equivariant · Year: · Authors: Cambridge (Csányi) / UBC (Ortner) — Batatia et al.
Higher-order equivariant message passing (4-body messages) that reaches SOTA accuracy with only 1-2 layers; later extended into the universal MACE-MP foundation model family.
License: MIT
Tags: equivariant, higher-order, architecture
Category: Equivariant · Year: · Authors: ICAMS
Graph Atomic Cluster Expansion: a foundation-scale implementation of ACE with explicit multi-body basis functions for wide-coverage materials modelling.
License: Apache-2.0
Tags: equivariant, ACE, graph, foundation model
Category: Transformer · Year: · Authors: Orbital Materials
Non-equivariant, non-conservative graph neural network potential systematically trading off roto-equivariance, conservatism, and graph sparsity for >10x latency and >8x memory reduction at near-SOTA accuracy on large periodic systems.
License: Apache-2.0
Tags: transformer, throughput, torch.compile
Category: Transformer · Year: · Authors: Orbital Materials
Predecessor to Orb-v3. A non-equivariant graph network exploring trade-offs between accuracy and inference cost on materials simulation; trained on MPTrj + Alexandria with rotation-invariance learnt rather than imposed.
License: Apache-2.0
Tags: learnt-equivariance, graph, foundation
Category: Transformer · Year: · Authors: Orbital Materials
Orb-v3 variant for molecules, electrolytes, metal complexes, and biomolecules, trained on the ~100M-structure OMol25 dataset with explicit total-charge and spin-multiplicity conditioning.
License: Apache-2.0
Tags: transformer, charge-aware, spin-aware, foundation model
Paper: https://www.orbitalmaterials.com/posts/orbmol-extending-orb-to-molecular-systems
Category: Transformer · Year: · Authors: Orbital Materials
Second-generation OrbMol adding learnable per-atom electrostatics to the OrbMol molecular potential: a LatentChargeHead predicts per-atom latent charges constrained to the system total charge, and a CoulombModule adds long-range Coulomb energy (direct summation for non-periodic systems, particle-mesh Ewald for periodic ones). Trained on OMol25 and OPoly26 at the ωB97M-V/def2-TZVPD level.
License: Apache-2.0
Tags: transformer, charge-aware, spin-aware, long-range-electrostatics, molecular
Category: Equivariant · Year: · Authors: Thomas et al.
First E(3)-equivariant convolutional architecture for point clouds, introducing spherical-harmonic tensor products that underlie nearly all modern equivariant MLIPs (NequIP, MACE, Equiformer).
License: MIT
Tags: equivariant, E(3), tensor field, point cloud
Paper: https://arxiv.org/abs/1802.08219
Code: https://github.com/tensorfieldnetworks/tensorfieldnetworks
Category: Transformer · Year: · Authors: Fuchs et al.
Self-attention generalized to SE(3)-equivariant inputs via tensor field attention; an early blueprint for equivariant transformer architectures like Equiformer.
License: MIT
Tags: transformer, SE(3), self-attention, equivariant
Paper: https://arxiv.org/abs/2006.10503
Code: https://github.com/FabianFuchsML/se3-transformer-public
Category: Transformer · Year: · Authors: Shoghi et al. (CMU / Meta)
Joint Multi-domain Pre-training: a strategy that trains one shared GemNet-OC backbone simultaneously on OC20, OC22, ANI-1x and Transition-1x (~120M systems), demonstrating multi-dataset pretraining for transferable potentials — a precursor to the universal MLIP foundation models that followed.
License: CC-BY-NC-4.0
Tags: transformer, multi-task pretraining, foundation model
Category: Equivariant · Year: · Authors: Meta FAIR
Equivariant Smooth Energy Network: conservative-force equivariant GNN with a smooth potential energy surface designed for stable long-horizon MD. Serves as the backbone underneath Meta's UMA foundation model.
License: MIT
Tags: equivariant, smooth PES, foundation model
Category: Transformer · Year: · Authors: Meta FAIR
Universal Model for Atoms: a Mixture of Linear Experts (MoLE) foundation model built on the eSEN backbone, trained on ~500M structures spanning OC20, ODAC23, OMat24, OMC25, and OMol25. NeurIPS 2025 spotlight.
License: proprietary
Tags: transformer, mixture-of-experts, foundation model, charge-aware, spin-aware
Category: Equivariant · Year: · Authors: Koker & Smidt (MIT Atomic Architects)
Compact E(3)-equivariant foundation potential pairing a simplified NequIP design with equivariant RMS layer normalization and the Muon optimizer; 700K parameters trained in ~100 A100 GPU-hours, with ~20x lower training cost and two orders of magnitude faster inference than the top Matbench-Discovery models.
License: MIT
Tags: equivariant, JAX, foundation model, Muon optimizer
Category: Transformer · Year: · Authors: Pozdnyakov & Ceriotti (EPFL)
Point Edge Transformer: an unconstrained graph transformer for atomistic systems. Drops strict equivariance in favour of attention-based message passing on point-and-edge inputs, with rotation-invariance learnt from data rather than imposed by the architecture. Direct precursor to PET-MAD.
License: MIT
Tags: transformer, attention, learnt-equivariance
Category: Transformer · Year: · Authors: EPFL (Ceriotti lab)
Lightweight universal transformer-GNN potential (Point-Edge Transformer) trained on the Massive Atomistic Diversity (MAD) dataset spanning solids, surfaces, and molecules; competitive with larger uMLIPs across diverse atomistic systems.
License: BSD-3-Clause
Tags: transformer, PET, foundation model, lightweight
Category: Transformer · Year: · Authors: Liao et al. (MIT Atomic Architects)
Third-generation SE(3)-equivariant graph attention transformer with improved efficiency, expressivity, and generality; achieves the strongest results within the Equiformer family on OC20 S2EF-2M, MPtrj, OMat24, sAlex, and Matbench-Discovery.
License: MIT
Tags: transformer, SE(3)-equivariant, foundation model
Category: Equivariant · Year: · Authors: ACEsuit (Kovacs, Batatia, Csanyi et al.)
Polarisable electrostatic foundation model that augments MACE with a non-self-consistent polarisable field formalism, learning atomic charge and spin densities (Gaussian-type multipoles) directly from energies/forces; global charge/spin constraints are enforced via learnable Fukui equilibration functions. Trained on OMol25 (~100M structures at ωB97M-V), released in M (12 A) and L (18 A) receptive-field variants for molecular chemistry and non-covalent interactions.
License: MIT
Tags: equivariant, MACE, polarisable, charge-aware, spin-aware, long-range-electrostatics, foundation model
Category: Equivariant · Year: · Authors: Kuroda, Ishihara, Shiota, Mizukami (Osaka Univ. / QIQB)
Multi-domain universal MACE-architecture potential extending the MACE-Osaka series to 97 elements — the broadest elemental coverage to date — by integrating MACE-Osaka24's inorganic + organic data with the newly constructed HE26 heavy-element dataset of minor actinides assembled from experimental and computational literature. Targets nuclear and actinide chemistry while retaining strong performance on the inorganic MPtrj and organic OFF23 test sets.
License: MIT
Tags: MACE, foundation model, actinides, nuclear, 97 elements
Category: Equivariant · Year: · Authors: Bi, Zhao, Sun, Hu, Lu, Cheng (Shanghai University)
Efficient equivariant graph neural network MLIP that introduces a geometry-aware dual-path dynamic attention mechanism inside its message-passing layers and a physics-informed multi-perspective pooling strategy for global system representations. Demonstrates competitive accuracy with mainstream equivariant models at markedly lower computational cost across organic molecules (QM7, MD17), Li-containing crystals, two-dimensional materials (bilayer graphene, black phosphorus), surface catalytic reactions (formate decomposition), and charged systems, while remaining stable for long-time MD simulations.
Tags: equivariant, dynamic attention, efficient
Category: Equivariant · Year: · Authors: Zhang et al. (Shanghai AI Lab / CUHK)
Unified neural interatomic potential that embeds an Ewald-inspired reciprocal-space formulation inside an irreducible SO(3)-equivariant framework. Performs equivariant message passing in reciprocal space via learned equivariant k-space filters and an equivariant inverse transform, capturing anisotropic tensorial long-range correlations without sacrificing physical consistency; consistently improves energy and force accuracy, data efficiency, and long-range extrapolation across periodic systems, supramolecular assemblies, conjugated molecules, charged dimers, and biomolecular dynamics.
Tags: SO(3)-equivariant, long-range-electrostatics, reciprocal space, Ewald
Category: Transformer · Year: · Authors: Qu, Wood, Krishnapriyan, Ulissi (FAIR / Meta, UC Berkeley, LBNL)
Scalable, energy-conserving, attention-based MLIP that pairs local neighborhood self-attention with a global all-to-all node attention layer in which every atom attends to every other atom. The data-driven all-to-all component captures long-range interactions without explicit electrostatic priors and remains the most durable ingredient as data and model size scale to O(100M) training samples. Sits atop the OMol25 leaderboard at release while remaining competitive on OMat24 (materials) and OC20 (catalysts); cuts long-range distance-scaling error by ~90% versus the next-best foundation model, with stable long-timescale MD recovering experimental densities and heats of vaporisation.
License: MIT
Tags: transformer, all-to-all attention, long-range-electrostatics, foundation model, charge-aware, spin-aware
Category: Equivariant · Year: · Authors: Ho, van der Oord, Darby, Csányi, Ortner et al. (Cambridge / UBC / ACEsuit)
Equivariant many-body message-passing interatomic potential extending the MACE framework to magnetic materials by embedding atomic magnetic moments as explicit degrees of freedom alongside positions. Learns physically consistent and transferable representations of magnetic behaviour beyond collinear approximations and can incorporate spin-orbit coupling, achieving near density-functional-theory accuracy with strong data efficiency by fine-tuning from a pre-trained foundation model. Targets structural transformations, finite-temperature magnetic phenomena, and high-throughput screening of strongly spin-orbit coupled materials.
Tags: equivariant, MACE, magnetic moments, spin-orbit coupling
Category: Equivariant · Year: · Authors: Nascimento, Descoteaux, Zichi, Tan, Witt, Molinari, Mantha, Kitchaev, Kornbluth, Gadelrab, Tuffile, Kozinsky (Harvard / Bosch)
Multifidelity Mixture-of-Experts framework built on the strictly local E(3)-equivariant Allegro architecture. Spatially partitions the simulation domain into chemically complex regions (e.g. reactive interfaces) and simple regions (e.g. bulk lattices) and assigns Allegro experts of different capacity to each, enabling expensive high-fidelity inference only where required while a cheaper expert handles the rest of the cell.
Tags: equivariant, Allegro, mixture-of-experts, multifidelity, spatial partitioning
Category: Equivariant · Year: · Authors: Yin, Ouyang, Fan, Lin, Hu, Lv, Cao, Xiao, Chen, Ren (ByteDance Seed / Tsinghua / Peking University)
Hessian-informed machine learning interatomic potential trained with the Hessian-INformed Training (HINT) protocol — Hessian pre-training, configuration sampling, curriculum learning, and a stochastic projected Hessian loss — to attain Hessian-level accuracy with two to four orders of magnitude fewer high-fidelity Hessian labels than standard training. Substantially improves transition-state search and brings Gibbs free-energy predictions close to chemical accuracy in data-scarce regimes, and reproduces phonon renormalization and superconducting Tc of strongly anharmonic hydrides in close agreement with experiment.
Tags: Hessian, HINT, transition states, anharmonic, curvature-aware
Category: Transformer · Year: · Authors: Unke, Chmiela, Gastegger, Schütt, Sauceda, Müller
MLIP that explicitly captures electronic degrees of freedom and nonlocal effects, modelled via self-attention in a transformer architecture. Total charge and spin multiplicity are injected as global tokens that condition the local atomic embeddings — a direct conceptual ancestor of charge/spin-conditioned foundation models such as UMA and MACE-POLAR-1.
License: MIT
Tags: transformer, self-attention, charge-aware, spin-aware, long-range-electrostatics
Category: Transformer · Year: · Authors: Unke, Stöhr, Ganscha, Unterthiner, Maennel, Kashubin, Ahlin, Gastegger, Sandonas, Berryman, Tkatchenko, Müller
SpookyNet-based biomolecular force-field framework that combines top-down (whole-protein) and bottom-up (fragment) sampling to train transferable, quantum-accurate ML potentials for proteins and condensed-phase biomolecular dynamics.
License: proprietary
Tags: transformer, biomolecular, fragment sampling, charge-aware
Category: Descriptor · Year: · Authors: Behler & Parrinello
The Behler–Parrinello high-dimensional neural network potential — the 2007 paper that introduced symmetry functions and the atomic-decomposition framework underlying essentially every modern MLIP.
License: GPL-3.0-or-later
Tags: descriptor, atomic NN, symmetry functions, BPNN, HDNNP
Category: Descriptor · Year: · Authors: Drautz (ICAMS)
Atomic Cluster Expansion: a complete, systematically improvable many-body basis for the local atomic environment; the mathematical backbone of PACE/GRACE and a strong influence on MACE.
License: Apache-2.0
Tags: descriptor, ACE, many-body, linear basis
Category: Descriptor · Year: · Authors: Bartók, Payne, Kondor, Csányi (Cambridge)
Gaussian Approximation Potentials: a kernel-based MLIP fit to ab-initio energies and forces using SOAP-like many-body descriptors; the canonical kernel reference for descriptor-based potentials.
License: GPL-3.0-or-later
Tags: descriptor, kernel, SOAP, Gaussian process
Category: Descriptor · Year: · Authors: DeepModeling
Deep Potential Molecular Dynamics: local frame descriptors + deep networks giving ab-initio-level accuracy with linear scaling, widely used for large MD.
License: LGPL-3.0
Tags: descriptor, deep potential, local frame
Category: Descriptor · Year: · Authors: DeepModeling
Second-generation Deep Potential architecture with attention and multi-task heads, targeting a universal deep potential for diverse chemistries.
License: LGPL-3.0
Tags: descriptor, attention, multi-task, foundation model
Category: Descriptor · Year: · Authors: DeepModeling
Message-passing graph neural network built on a Line Graph Series (LiGS) that updates bond, angle, and dihedral representations while preserving energy conservation and physical symmetries; designed for Large Atomistic Models with clean scaling in model size, data, and compute. The DPA-3.1-3M variant trained on OpenLAM-v1 tops zero-shot generalization across 12 downstream tasks.
License: LGPL-3.0
Tags: descriptor, message-passing, line graph, foundation model
Category: Equivariant · Year: · Authors: Microsoft
Microsoft foundation MLIP using a Graphormer transformer backbone with explicit translation/periodic-boundary invariance and equivariant features for materials. Trained on large-scale ab-initio data spanning 0-5000 K and pressures up to 1000 GPa as a reusable simulator for materials discovery and high-throughput computation.
License: MIT
Tags: transformer, foundation model
Category: Descriptor · Year: · Authors: Chalmers (Fan group) / Liang et al.
Universal neuroevolution-potential foundation model spanning 89 elements across inorganic and organic materials, trained via separable natural evolution strategies and distributed in GPUMD for empirical-potential-like speed.
License: GPL-3.0
Tags: descriptor, neuroevolution, foundation model
Category: Equivariant · Year: · Authors: Zhejiang Univ. (Hou lab) / Su et al.
Equivariant network with Tensorized Quadrangle Attention (TQA) that captures three- and four-body interactions in linear time; pre-trained on nablaDFT and fine-tuned on SPICE as a quantum-accurate biomolecular force-field foundation model with ~10x faster inference than MACE-OFF.
License: MIT
Tags: equivariant, linear tensor, biomolecular, attention
Category: Invariant · Year: · Authors: Zhou et al. (CAS / UCAS)
Invariant foundation MLIP using a separable O(N) attention mechanism for three-body interactions; 10M-parameter models trained on OMat24 / MPTrj / sAlex match equivariant SOTA on Matbench-Discovery (F1 0.847) at >13x lower training cost than eSEN-30M-MP.
License: BSD-3-Clause
Tags: invariant, attention, foundation model
Category: Invariant · Year: · Authors: Zhou et al. (CAS / ICT, HPC-AI-Team)
Billion-parameter Mixture-of-Experts extension of MatRIS that inserts sparse expert modules around the self-attention layer — a message-update MoE for message construction and a feature-update MoE for post-attention refinement — with element-type routing that keeps the activated expert set time-independent and the potential energy surface continuous. Released in M (2.47B) and L (11.50B) variants and trained on heterogeneous domains (molecules, materials, catalysis, MOFs, and direct air capture) via the new Janus hybrid-parallel framework, attaining 1.0–1.2 EFLOPS at >90% parallel efficiency and compressing billion-parameter uMLIP training from weeks to hours on Exascale supercomputers.
License: BSD-3-Clause
Tags: invariant, mixture-of-experts, billion-parameter, multi-task, foundation model
Category: Descriptor · Year: · Authors: Thompson, Swiler, Trott, Foiles, Tucker (Sandia)
Spectral Neighbor Analysis Potential: a linear descriptor MLIP fit to bispectrum components of the local atomic environment, designed for high-throughput LAMMPS simulations. The canonical industrial-scale linear descriptor potential alongside GAP and MTP.
License: GPL-2.0
Tags: descriptor, linear, bispectrum
Category: Descriptor · Year: · Authors: Shapeev (Skoltech)
Moment Tensor Potentials: a systematically improvable linear MLIP based on contractions of moment tensors of the local environment. Pairs naturally with D-optimality / MaxVol active learning (Podryabinkin & Shapeev 2017), making the MTP family the canonical reference for AL-native potential fitting.
License: BSD-2-Clause
Tags: descriptor, linear, moment tensors, active-learning
Category: Descriptor · Year: · Authors: Chmiela, Sauceda, Poltavsky, Müller, Tkatchenko
Symmetric Gradient-Domain Machine Learning: a kernel ridge regression force field fit directly in the gradient domain, with energy obtained by closed-form integration. Strong on small molecules where rigorous symmetry handling is critical.
License: MIT
Tags: descriptor, kernel, gradient-domain
Category: Descriptor · Year: · Authors: Vandermause, Torrisi, Batzner, Sun, Kolpak, Kozinsky (Harvard)
Fast Learning of Atomistic Rare Events: a Gaussian-process-regression Bayesian potential trained on-the-fly during MD, with GP-uncertainty driving when to call DFT vs. trust the surrogate. Includes tabulated/mapped force-field export for production-speed MD; principal kernel-based AL framework and immediate predecessor of the Kozinsky group's NequIP/Allegro line.
License: MIT
Tags: descriptor, Gaussian process, active-learning, Bayesian
Category: Descriptor · Year: · Authors: Zubatyuk, Smith, Leszczynski, Isayev
Original Atoms-in-Molecules Network: a self-consistent message-passing potential that propagates atomic environment vectors through repeated neighbour updates, learning charge-aware atomic representations for organic chemistry. The conceptual precursor to AIMNet-NSE and AIMNet2.
License: MIT
Tags: descriptor, message-passing, AIM
Paper: https://pubs.rsc.org/en/content/articlehtml/2019/sc/c9sc00531e
Category: Descriptor · Year: · Authors: Zubatyuk, Smith, Nebgen, Tretiak, Isayev
Neural Spin Equilibration variant of AIMNet that handles arbitrary total charge and spin multiplicity through an SCF-like message-passing loop, predicting transferable atomic charges and spins. The conceptual ancestor of charge/spin-conditioned models like AIMNet2 and SpookyNet.
License: MIT
Tags: descriptor, message-passing, charge-aware, spin-aware, SCF
Category: Invariant · Year: · Authors: Lubbers, Smith, Barros (LANL)
Hierarchically Interacting Particle Neural Network: a message-passing potential that decomposes atomic energies into a hierarchy of n-body terms with explicit residual structure, providing both interpretable hierarchical decomposition and natural uncertainty estimates from the residual stack.
License: BSD-3-Clause
Tags: invariant, message-passing, hierarchical, uncertainty
Paper: https://pubs.aip.org/aip/jcp/article/148/24/241715/962591
Category: Descriptor · Year: · Authors: Devereux, Smith, Huddleston, Barros, Zubatyuk, Isayev, Roitberg
ANI variant extending coverage to seven elements (H, C, N, O, S, F, Cl); widely used in drug discovery for fast geometry and energy scans on organic chemistry.
License: MIT
Tags: descriptor, atomic NN, symmetry functions
Category: Descriptor · Year: · Authors: Smith, Isayev, Roitberg
Original ANI: an atomistic neural network potential built on Behler-style symmetry function descriptors and per-element atomic networks, trained on ~22M DFT structures of organic molecules covering H, C, N, O.
License: MIT
Tags: descriptor, atomic NN, symmetry functions
Paper: https://pubs.rsc.org/en/content/articlehtml/2017/sc/c6sc05720a
Category: Descriptor · Year: · Authors: Smith, Nebgen, Lubbers, Isayev, Roitberg
Active-learned extension of ANI-1: applies query-by-committee active learning to grow the training set towards a chemically diverse organic-molecule sampling, dramatically improving generalisation while maintaining ANI-style efficiency.
License: MIT
Tags: descriptor, atomic NN, active-learning
Paper: https://pubs.aip.org/aip/jcp/article/148/24/241733/962534
Category: Descriptor · Year: · Authors: Smith, Nebgen, Zubatyuk, Lubbers, Devereux, Barros, Tretiak, Isayev, Roitberg
ANI-1x transfer-learned to a CCSD(T)/CBS-quality reference, yielding a near-coupled-cluster-accuracy organic-chemistry potential at deep-network speed. The first widely deployed example of using transfer learning to push beyond DFT.
License: MIT
Tags: descriptor, atomic NN, transfer learning, CCSD(T)
Category: Descriptor · Year: · Authors: Anstine, Zubatyuk & Isayev (CMU)
Second-generation Atoms-in-Molecules Network potential covering 14 elements (H, B, C, N, O, F, Si, P, S, Cl, As, Se, Br, I) in neutral and charged states; combines ML-parameterised short-range terms with physics-based long-range electrostatics, trained on ~20M hybrid-DFT (wB97M-D3) calculations for routine use as a DFT replacement in organic and elemental-organic chemistry.
License: MIT
Tags: descriptor, AIM, charge-aware, long-range-electrostatics
Category: Equivariant · Year: · Authors: Farr, Doerr, Mirarchi, Sabanés Zariquiey & De Fabritiis (Acellera Labs / UPF Barcelona)
Drug-discovery-oriented MLIP built on the TensorNet2 architecture — a refined vector–scalar equivariant TensorNet that adds scalar partial-charge features, performs neutral charge equilibration, and includes a long-range Coulomb energy term. Pretrained on a large dataset of drug-like compounds covering H, B, C, N, O, F, Si, P, S, Cl, Br, I in neutral and charged states; balances DFT-level accuracy on torsion scans, MD trajectories, and batched minimisations with high-throughput inference suitable for FEP and lead-optimisation workflows.
License: Apache-2.0
Tags: TensorNet2, drug discovery, charge-aware, long-range-electrostatics
Category: Invariant · Year: · Authors: Schütt et al.
Continuous-filter convolutional network that introduced smooth, translation-invariant filters for molecules; the baseline for many later invariant message-passing potentials. Predicts energies and forces with all-atom symmetry preserved.
License: MIT
Tags: invariant, message-passing, continuous-filter convolution
Paper: https://arxiv.org/abs/1706.08566
Code: https://github.com/atomistic-machine-learning/schnetpack
Category: Invariant · Year: · Authors: Gasteiger et al.
Directional message passing network with spherical basis functions that explicitly encode bond angles, improving data efficiency over SchNet-style models. The original paper (arXiv:2003.03123) introduced the directional MP framework; the follow-up DimeNet++ (arXiv:2011.14115) refined it with faster, uncertainty-aware variants.
License: Hippocratic-2.1
Tags: invariant, message-passing, directional, spherical
Category: Equivariant · Year: · Authors: TUM / OC20
High-capacity spherical message-passing architecture used in the OC20/OC22 benchmarks; very strong for catalyst adsorption and surface chemistry.
License: MIT
Tags: equivariant, message-passing, spherical
Category: Equivariant · Year: · Authors: Schütt et al.
Polarizable Atom Interaction Neural Network: uses coupled scalar/vector features to capture forces and dipoles with E(3) equivariance at lower cost than full tensors.
License: MIT
Tags: equivariant, vector, scalar, polarizable
Paper: https://arxiv.org/abs/2102.03150
Code: https://github.com/atomistic-machine-learning/schnetpack
Category: Equivariant · Year: · Authors: Seoul Nat. Univ.
NequIP-based scalable equivariant graph neural network potential with parallel-MD optimisations (LAMMPS GPU support), enabling very large equivariant simulations while retaining E(3)-equivariance.
License: MIT
Tags: invariant, speed-optimized, NequIP-derived
Category: Invariant · Year: · Authors: NIST
Atomistic Line Graph Neural Network: augments the atomic graph with a line graph so bond angles and higher-order interactions are encoded explicitly.
License: Unlicense
Tags: invariant, line graph, directional
Category: Invariant · Year: · Authors: Materials Virtual Lab
Materials Graph Network with 3-body interactions; trained on Materials Project relaxations to give a universal potential over most of the periodic table.
License: BSD-3-Clause
Tags: invariant, foundation model
Category: Invariant · Year: · Authors: Berkeley (Ceder group)
Charge-aware graph neural network that extends M3GNet with oxidation state and local charge features; particularly strong for battery and redox-active materials.
License: BSD-3-Clause
Tags: invariant, charge-aware, foundation model
Category: Equivariant · Year: · Authors: Seoul Nat. Univ. (MDIL-SNU)
Lightweight universal MLIP distilled from the SevenNet-Omni teacher, delivering over an order-of-magnitude speedup while retaining broad transferability for scalable atomistic simulations on thousands of atoms.
License: MIT
Tags: invariant, distilled, lightweight, universal MLIP
Category: Equivariant · Year: · Authors: Seoul Nat. Univ. (MDIL-SNU)
Multi-fidelity universal foundation MLIP built on the SevenNet-MF backbone and trained on 15 open datasets (~250M structures across molecules, crystals, and surfaces); serves as the teacher model for SevenNet-Nano.
License: MIT
Tags: invariant, multi-fidelity, foundation model
Category: Transformer · Year: · Authors: Preferred Networks / Matlantis
Eighth release of the Preferred Potential: a universal MLIP trained on a large r2SCAN meta-GGA dataset, capable of reproducing 45 elements off-the-shelf across crystals, molecules, surfaces, and adsorption structures without fine-tuning. Distributed commercially via the Matlantis SaaS platform.
License: proprietary
Tags: transformer, foundation model, r2SCAN
Category: Descriptor · Year: · Authors: Chen et al. (NEP framework)
Universal organic force field for C, H, O, N, S, P built within the Neuroevolution Potential (NEP) framework. Trained on a chemically rich dataset assembled through a unified top-down/bottom-up sampling strategy, providing a balanced description of bond breaking/formation, aromatic growth, hydrogen bonding, van der Waals interactions, and π-stacking; reaches near-DFT force accuracy while running ~200x faster than ReaxFF on identical hardware, enabling hundreds-of-nanoseconds reactive MD.
License: GPL-3.0
Tags: descriptor, neuroevolution, reactive, organic
Category: Descriptor · Year: · Authors: Martyka, Tong, Jankowska, Dral (Xiamen University)
First universal neural network potential for molecular ground and excited electronic states. An ensemble of MS-ANI-style invariant potentials trained on PubChemQC TD-DFT (B3LYP/6-31+G*) excited-state data combined with CCSD(T)/CBS ground-state energies from ANI-1ccx, with a separate head predicting oscillator strengths of interstate transitions. Approaches TD-DFT accuracy for UV/vis spectra and photodynamics at a fraction of the cost while outperforming semiempirical methods.
License: MIT
Tags: excited states, photodynamics, ensemble
Paper: https://chemrxiv.org/doi/10.26434/chemrxiv-2025-j207x
Category: Equivariant · Year: · Authors: Picha, Karwounopoulos, Erhard, Boresch, Heid (TU Wien / U. Vienna)
GRACE-architecture MLIP for organic systems, trained on the SPICE v2.0 dataset and integrated with ASE for MD. Two-layer GRACE-OFF models outperform MACE-OFF (including MACE-OFF24(M)) on single-point energies, forces, torsional profiles, and condensed-phase properties of organic liquids and water; for water and hexane they also beat the much more expensive UMA(S) on densities and radial distribution functions. Established as an accurate, GPU-efficient foundation potential for organic-liquid and biomolecular MD.
License: MIT
Tags: organic liquids, GRACE, condensed phase, reactive
Category: Transformer · Year: · Authors: Elsharkawy, Mikuni, Bhimji, Nachman (LBNL / NERSC)
Transformer-based small-molecule MLIP that adapts the Omnilearned Point-Edge-Transformer (PET) foundation model — pre-trained on ~1 billion LHC particle jets — to molecular dynamics via cross-domain transfer learning. Uses an interaction-matrix attention bias to inject pairwise atomic physics into transformer attention; on the OMol25 dataset OmniMol-M outperforms a 1B-parameter baseline transformer with ~20× fewer parameters, demonstrating the first cross-discipline transfer for scientific point-cloud foundation models.
Tags: transformer, cross-domain transfer, PET
Category: Equivariant · Year: · Authors: Yan, Bohde et al. (Texas A&M, divelab/AIRS)
Hybrid Invariant–Equivariant materials foundation potential that interleaves invariant and O(3)-equivariant message-passing layers to leverage invariant-layer scalability while reserving equivariant layers for high-order interactions. Force and stress are obtained as exact derivatives of a conservative energy, and the model achieves SOTA on Matbench Discovery while running ~90% faster than SevenNet-l3i5 and ~140% faster than EquiformerV2.
License: GPL-3.0
Tags: equivariant, hybrid invariant-equivariant, foundation model
Category: Equivariant · Year: · Authors: Batatia, Lin, Hart, Kasoar, Elena, Norwood, Wolf, Csányi (Cambridge / ACEsuit)
Cross-learning multi-head MACE foundation model that bridges molecular, surface, and inorganic crystal chemistry in a single MLIP. Enhances the MACE architecture with stronger element-weight sharing and non-linear tensor-decomposition product bases, then post-trains a multi-head replay scheme on OMAT-24 (PBE crystals), MPTraj, OMol (ωB97M-VV10), OC20 (surfaces), SPICE, RGD1, and MATPES-r2SCAN heads to unify electronic-structure theories.
License: MIT
Tags: equivariant, MACE, multi-head, cross-domain, foundation model
Category: Invariant · Year: · Authors: Chang, Zhu (Wuhan University of Technology)
Moment Graph Neural Network: rotation-invariant message-passing architecture whose node and edge updates operate on Cartesian moment representations of 3D molecular graphs, capturing high-order angular structure without explicit equivariant tensor products. Reaches SOTA on QM9 and revised MD17 (incl. MD17-ethanol) and generalises to 3BPA and 25-element high-entropy alloys, including amorphous-electrolyte MD.
Tags: invariant, moment representation, molecular potential
Category: Equivariant · Year: · Authors: Lupo Pasini, Choi et al. (ORNL / NERSC)
Exascale multi-task atomistic graph foundation model built on the HydraGNN framework, with a PaiNN-based message-passing backbone selected via large-scale DeepHyper hyperparameter optimization on Frontier. Jointly pre-trained on 16 open first-principles datasets (~544M structures, 85+ elements) using shared message-passing layers and per-dataset output heads, scaled to 16,000 GPUs and able to evaluate 1.1 billion atomistic structures in 50 seconds for downstream materials screening.
License: BSD-3-Clause
Tags: equivariant, PaiNN, multi-task, exascale, foundation model
Category: Descriptor · Year: · Authors: Fan, Tang, Berger, Fransson, Xu, Erhart et al. (GPUMD)
Charge-aware extension of the neuroevolution potential (NEP) framework that introduces explicit, environment-dependent partial charges represented per-ion by neural networks of the local descriptor vector. Implemented in GPUMD with both Ewald and particle-particle particle-mesh electrostatics, enabling Born-effective-charge tensors, dielectric properties, and infrared spectra alongside long-range MD scalable to million-atom systems on consumer GPUs.
License: GPL-3.0
Tags: descriptor, neuroevolution, charge-aware, Ewald, long-range
Category: Transformer · Year: · Authors: Mazitov, Bigi, Kellner, Pegolo, Tisi, Pozdnyakov, Loche, Kazeev, Fraux, Ceriotti et al. (EPFL / lab-cosmo)
Successor to PET-MAD: a generally applicable r²SCAN universal interatomic potential that extends elemental coverage to 102 elements via the curated MAD-1.5 dataset (~217k structures). Same Point Edge Transformer (PET) backbone with rotation-invariance learnt from data, retrained at the r²SCAN meta-GGA level with targeted enrichment strategies (molecules, clusters, surfaces, low-dimensional structures, bulk crystals) and uncertainty-quantification-driven outlier removal. Reported as more robust, more accurate, and faster than the original PET-MAD across challenging molecular dynamics benchmarks.
License: BSD-3-Clause
Tags: transformer, PET, foundation model, r²SCAN, 102 elements
Category: Equivariant · Year: · Authors: Lewis-Atwell, Saiz Pardo, Rieu, Loche, Bocus, Cersonsky, Ceriotti et al.
Density-first machine-learned electronic-structure framework that learns the Hohenberg-Kohn map from nuclear configurations to the ground-state electron density using an SE(3)-equivariant neural network predicting density coefficients of an atom-centred Gaussian basis, with a Δ-learning prior built from superposed atomic densities. A second equivariant network then maps the predicted density to the total energy, providing a unified framework for molecular dynamics, energies, forces, and electronic observables (dipole moments, polarizabilities, infrared spectra). Validated on ethanol, ethanethiol, resorcinol, and polythiophene oligomers (extrapolating from 1-6 to 12 monomers).
Tags: equivariant, SE(3), electron density, Δ-learning, spectroscopy
Category: Transformer · Year: · Authors: Bigi, Pegolo, Mazitov, Ceriotti (EPFL / lab-cosmo)
Extra-large variant of the Point Edge Transformer (PET) trained with an OMat24 + sAlex + MPtrj recipe (the OAM data mixture). Pushes the limits of unconstrained MLIPs by trading explicit E(3) symmetry constraints for capacity, depth, and data, achieving the top position on the Matbench Discovery leaderboard at release. Configuration: d_pet 640, d_node 2560, 5 GNN layers + 3 attention layers, 10 Å cutoff with adaptive 40-neighbour cap, distributed via the upet package alongside the wider PET-MAD / PET-OMat / PET-SPICE family.
License: BSD-3-Clause
Tags: transformer, PET, unconstrained, foundation model, Matbench Discovery
Category: Equivariant · Year: · Authors: Yin, Zhang, Yang et al.
Local-frame-based equivariant interatomic potential that builds atom-centred frames with learnable geometric transitions, replacing the spherical-harmonic tensor products used by NequIP/MACE-style models with cheaper Cartesian-frame operations. Achieves SOTA accuracy and improved efficiency on Matbench Discovery and OC2M benchmarks across molecular reactions, crystal stability, and surface catalysis, with an OMat24-pretrained foundation variant (alphanet-v1-oam) released on the Matbench Discovery leaderboard.
License: MIT
Tags: equivariant, local frame, foundation model
Category: Equivariant · Year: · Authors: Xu et al.
Tensor Atomic Cluster Expansion: a unified Cartesian-space framework that decomposes atomic environments into a complete hierarchy of irreducible Cartesian tensors, providing symmetry-consistent invariant and equivariant representations without spherical-harmonic Clebsch-Gordan overhead. Universal embeddings expose computational level, total charge, magnetic moments, and external-field perturbations as conditioning inputs, while a Latent Ewald Summation module handles long-range electrostatics. Released with an OMat24-pretrained foundation variant (tace-v1-oam-m) on the Matbench Discovery leaderboard, with TorchSim, LAMMPS-ML-IAP, and ASE calculators.
License: MIT
Tags: equivariant, ACE, Cartesian tensors, long-range, charge-aware, magnetic, foundation model
Category: Transformer · Year: · Authors: Elhag, Raja, Morehead, Blau, Zhao, Tyrchan, Nittinger, Morris, Bronstein (Oxford / LBNL / AstraZeneca / AITHYRA)
Transformer-based interatomic potential built on a generic, non-equivariant backbone that learns SO(3)-equivariance implicitly through a latent equivariance training objective rather than via architectural constraints. Replaces graph-based inductive biases and Clebsch-Gordan tensor products with a scalable embedding-space alignment loss, achieving 40–60% improvement over a data-augmentation baseline across varying OMol25 training-set sizes. Released with a TransIP-L checkpoint on Hugging Face and built on top of the fairchem framework.
License: MIT
Tags: transformer, non-equivariant, latent equivariance, fairchem
Category: Transformer · Year: · Authors: Li, Huang, Ding, Wang, Wei, Yang, Wang, Liu, Shi, Jin, Zhang, Gerstein, Qin (Microsoft Research / Yale)
Efficient and equivariant transformer that replaces conventional SO(3) spherical-tensor-product convolutions with a Wigner 6j convolution (Wigner 6j Conv), shifting the dominant compute from edges to nodes and reducing tensor-product complexity from O(|E|) to O(|V|) while preserving E(3) equivariance and expressive power. Achieves a 7×–30× speedup over standard SO(3) convolutions on benchmark interatomic-potential tasks (OC20, OC22, SPICE, MD17/MD22) at chemical accuracy. Released as a NeurIPS 2025 Spotlight and serves as the architectural foundation for the later E2Former-V2 / UBio-MolFM line.
License: MIT
Tags: transformer, equivariant, attention, Wigner 6j, linear-scaling
Category: Transformer · Year: · Authors: Huang, Jiang, Liu, Wang, Zhao, Wang, Lu, Huang, Cheng, Du, Zhang (UBio Team, IQuest Research)
Universal molecular foundation model engineered for biomolecular systems, combining three components: (i) UBio-Mol26, a ~17M-configuration bio-specific dataset built via a multi-fidelity two-pronged strategy that combines systematic bottom-up enumeration with top-down sampling of native protein environments up to ~1,200 atoms (proteins, nucleic acids, lipids, drug-like molecules, biologically important ions and metals); (ii) E2Former-V2, a linear-scaling equivariant transformer integrating Equivariant Axis-Aligned Sparsification (EAAS) and Long-Short Range (LSR) modelling for ~4× higher inference throughput on large systems; and (iii) a three-stage curriculum-learning protocol going from energy initialisation to energy-force consistency and multi-fidelity refinement. Targets ab-initio-level fidelity on out-of-distribution biomolecular systems up to ~1,500 atoms.
Tags: transformer, equivariant, attention, bio-systems, foundation model, E2Former-V2
Category: Equivariant · Year: · Authors: Plé, Adjoua, Benali, Posenitskiy, Villot, Lagardère, Piquemal (Sorbonne Université / Qubit Pharmaceuticals)
Force-field-enhanced foundation MLIP for drug design built on the FENNIX hybrid framework: an Allegro E(3)-equivariant local embedding (256 scalar features, 16 equivariant channels up to l_max=2, three interaction layers, 5.3 Å cutoff) coupled with physics-grounded energy terms — short-range ZBL repulsion, Coulomb electrostatics with fluctuating atom-centred charges, and explicit dispersion. Trained on an extended SPICE2 synthetic-QM dataset and integrated with Tinker-HP for reactive molecular dynamics including quantum nuclear effects. Sets a new sub-kcal/mol standard on the Freesolv hydration-free-energy benchmark and supports protein folding, protein-ligand binding free energies, and chemical reactions.
License: LGPL-3.0
Tags: equivariant, force-field-enhanced, biomolecular, drug design, foundation model, JAX, charge-aware
Category: Invariant · Year: · Authors: Schütt, Arbabzadah, Chmiela, Müller, Tkatchenko
Deep Tensor Neural Network — the direct precursor to SchNet that introduced learned per-element embeddings refined by tensorised pairwise interaction blocks for quantum-chemical energies on QM9-style organic molecules.
License: MIT
Tags: invariant, tensor, deep network, precursor to SchNet
Category: Invariant · Year: · Authors: Xie & Grossman (MIT)
Crystal Graph Convolutional Neural Network — the first GNN built explicitly on periodic crystal graphs with multi-edge bond convolutions. Foundational ancestor of nearly every later universal materials GNN (MEGNet / M3GNet / CHGNet) and a workhorse for materials property prediction.
License: MIT
Tags: invariant, crystal graph, convolutional, precursor
Category: Invariant · Year: · Authors: Unke & Meuwly (Basel)
Modular invariant message-passing potential that simultaneously predicts energies, forces, dipole moments, and partial charges with explicit electrostatic and dispersion energy terms. One of the first MLIPs that handled molecules with non-zero net charge through learnable atomic charges plus Coulomb correction.
License: MIT
Tags: invariant, message-passing, charge-aware, electrostatics
Category: Invariant · Year: · Authors: Chen, Ye, Zuo, Zheng, Ong (UCSD / Materials Virtual Lab)
MatErials Graph Network — universal graph network with global state attributes that unifies molecules and crystals in one framework. Direct architectural ancestor of M3GNet/CHGNet from the same group; widely used for materials property prediction.
License: BSD-3-Clause
Tags: invariant, graph network, global attributes, materials
Paper: https://pubs.acs.org/doi/10.1021/acs.chemmater.9b01294
Category: Equivariant · Year: · Authors: Anderson, Hy, Kondor (Chicago)
Covariant Molecular Neural Network — an early end-to-end SO(3)-equivariant architecture using Clebsch-Gordan tensor products on irreducible representations of irreducible spherical tensors. Predates and informs the TFN/NequIP-style equivariant message-passing potential family.
License: Custom (research)
Tags: equivariant, SO(3), Clebsch-Gordan, tensor product
Category: Equivariant · Year: · Authors: Satorras, Hoogeboom, Welling (UvA)
E(n)-Equivariant Graph Neural Network: a simple, scalar-only equivariant architecture that achieves rotation/translation equivariance without higher-order tensor representations. Highly cited for its simplicity and broadly applied beyond MLIPs to generative modelling, protein structure, and dynamics.
License: MIT
Tags: equivariant, scalar, lightweight, E(n)
Category: Descriptor · Year: · Authors: Fan, Wang, Ying et al. (Aalto / GPUMD)
Original Neuroevolution Potential — a per-element neural network on local descriptors trained with separable natural-evolution strategies rather than gradient descent. Designed for raw GPU throughput in the GPUMD code; ancestor of NEP89, qNEP, and ORION.
License: GPL-3.0
Tags: descriptor, neuroevolution, GPU MD, GPUMD
Category: Invariant · Year: · Authors: Takamoto et al. (Preferred Networks)
Original Preferred Potential — first universal NNP covering 45 elements and the foundation of the commercial Matlantis SaaS platform. Predated the academic universal MLIP wave (M3GNet, CHGNet, MACE-MP) by over a year and demonstrated viable industrial-scale deployment.
License: proprietary
Tags: invariant, TeaNet, foundation model, Matlantis
Category: Transformer · Year: · Authors: Liao & Smidt (MIT Atomic Architects)
Original Equivariant Graph Attention Transformer — combines graph attention with TFN-style E(3)-equivariant tensor representations and depthwise tensor-product MLPs. Direct ancestor of Equiformer V2 and V3; influential for attention-based equivariant MLIPs.
License: MIT
Tags: transformer, equivariant, attention, TFN-style
Category: Transformer · Year: · Authors: Zitnick, Das, Goyal et al. (Meta FAIR)
Spherical Channels Network — represents atomic environments as multichannel spherical signals rotated into edge-aligned local frames, enabling efficient high-degree representations for OC20-class catalyst modelling. Direct precursor to eSCN and the Meta FAIR equivariant-transformer line.
License: MIT
Tags: equivariant, spherical channels, edge frames
Category: Equivariant · Year: · Authors: Frank, Unke, Müller (TU Berlin)
SO(3)-equivariant attention on arbitrary length scales: factorises equivariant tensor products into invariant scalar attention plus an equivariant filter, enabling long-range-capable equivariant transformers. Foundation of the later SO3LR molecular response model.
License: MIT
Tags: equivariant, attention, long-range, SO(3)
Category: Equivariant · Year: · Authors: Wang, Zhao, Cui et al. (Microsoft Research)
Vector-scalar interactive message passing potential that captures geometric information through coupled scalar and vector channels without explicit higher-order tensor algebra. Combines competitive accuracy on QM9/MD17/MD22 with practical efficiency for biomolecular MD.
License: MIT
Tags: equivariant, vector-scalar, biomolecular
Category: Descriptor · Year: · Authors: Zhang, Bi et al. (DeepModeling)
First-generation Deep Potential with Attention — pretrained Deep Potential descriptor model that introduces an attention layer to the DeepMD framework, enabling cross-domain transfer learning. Direct bridge between DeepMD and DPA-2 in the DeepModeling lineage.
License: LGPL-3.0
Tags: descriptor, attention, pretrained, DeepMD
Category: Transformer · Year: · Authors: Passaro & Zitnick (Meta FAIR)
Reduces SO(3) tensor-product convolutions to SO(2) by aligning each pair to a common rotation axis, dramatically lowering the cost of high-degree equivariant convolutions. Direct precursor to Equiformer V2's higher-degree backbone and key SOTA on OC20 in 2023.
License: MIT
Tags: equivariant, SO(3)→SO(2), high-degree
Category: Equivariant · Year: · Authors: Kovács, Moore, Browning, Batatia, Horton et al.
Transferable MACE force field for organic molecules covering 10 elements (H, C, N, O, F, P, S, Cl, Br, I) trained on SPICE quantum-chemistry data. The molecular sibling of MACE-MP-0 and template for later GRACE-OFF; widely used as a drop-in replacement for classical biomolecular force fields.
License: MIT
Tags: equivariant, organic FF, MACE family, biomolecular
Category: Invariant · Year: · Authors: Merchant, Batzner, Schoenholz, Aykol, Cheon, Cubuk (Google DeepMind)
Graph Networks for Materials Exploration — published in Nature 624, 80 (2023), demonstrated discovery of 2.2M new crystal structures (380k stable) via active-learning-coupled NNP-driven materials search. Established graph-network MLIPs as a viable engine for autonomous crystal discovery at scale.
License: Apache-2.0
Tags: invariant, graph network, materials discovery, active learning
Paper: https://www.nature.com/articles/s41586-023-06735-9
Code: https://github.com/google-deepmind/materials_discovery
Category: Equivariant · Year: · Authors: Batatia, Benner, Chiang, Elena, Kovács et al.
First MACE foundation model — a single MACE-architecture potential trained on the Materials Project trajectory dataset (MPtrj) covering 89 elements. Demonstrated broadly transferable accuracy across inorganic crystals, surfaces, defects, and molecular crystals; the reference universal MACE model and ancestor of MACE-Osaka26 / MACE-MH-1 / MACE-Magnetic / MACE-POLAR-1.
License: MIT
Tags: equivariant, foundation model, universal, MACE family
Category: Invariant · Year: · Authors: Weber et al. (Schrödinger Inc. / Columbia University)
Message Passing Network with Iterative Charge Equilibration: an invariant message-passing MLFF that decomposes the total energy into atom-centred contributions and, after every message-passing block, predicts atomic partial charges via a charge-equilibration (Qeq) approximation that feeds back into the next block. Explicit long-range Coulomb electrostatics on top of the equilibrated charges captures polarisation, charge transfer, and multiple oxidation states while remaining 5-20x faster than comparable-accuracy models. Released with pre-trained MPNICE models spanning 89 elements for organic liquids, molecular crystals, and bulk inorganic systems.
License: proprietary
Tags: invariant, charge-aware, iterative charge equilibration, long-range-electrostatics
Category: Descriptor · Year: · Authors: Chen & Dral (Xiamen University)
First-ever universal interatomic potential that simultaneously learns and predicts at multiple quantum-chemical levels of theory through a multi-fidelity AIO-ANI training strategy. Combines low- and high-level reference data (semiempirical, DFT, and coupled cluster) into a single network so the same model can deliver predictions across QC levels of organic chemistry with accuracy comparable to GFN2-xTB and double-zeta DFT, while being orders of magnitude faster. Released as part of the MLatom ecosystem with model weights and code in the dralgroup/aio-ani repository; the immediate predecessor to OMNI-P2x for excited states.
License: MIT
Tags: multi-fidelity, universal, ANI family, AIO-ANI
Category: Equivariant · Year: · Authors: Reschützegger, Aykent, Perin, Nunes, Cipcigan, Ferreira, Steiner et al. (IBM Research / U. São Paulo / Politecnico Milano)
Equivariant message-passing interatomic potential that replaces Clebsch-Gordan tensor products with cheaper geometric operations while keeping E(3) equivariance, and bakes in physical priors (ZBL short-range repulsion, smooth attenuation) so the learned potential energy surface stays smooth and well-behaved across the entire bond-length range. The Geodite-MP variant is trained on the Materials Project trajectory dataset (~160k inorganic crystal structures) and matches the accuracy of leading tensor-product foundation potentials on stability prediction, phonon-derived properties, thermal conductivity, and nanosecond MD, while running 3-5x faster than models with comparable accuracy.
License: MIT
Tags: equivariant, no tensor products, smooth PES, ZBL, foundation model
Category: Equivariant · Year: · Authors: Rumiantsev, Langer, Sodjargal, Ceriotti, Loche (EPFL lab-cosmo)
Equivariant message-passing interatomic potential built around equivariant — rather than scalar — charges for long-range interactions. Unlike standard cutoff-based MLIPs that fail to capture electrostatics, dispersion, or electron delocalisation, LOREM propagates equivariant charges through a long-range message-passing mechanism that captures orientation-dependent interactions without requiring per-dataset tuning of interaction cutoffs or message-passing depth. Implemented in JAX/Flax on top of e3x and jax-pme, LOREM is competitive with or surpasses prior scalar-charge long-range MLIPs across long-range benchmark datasets. Accepted at TMLR.
License: BSD-3-Clause
Tags: equivariant, long-range, equivariant charges, JAX, e3x, jax-pme
Category: Equivariant · Year: · Authors: Zhang & Guo (University of New Mexico)
Node-equivariant message-passing graph neural network that reformulates equivariant message passing from edges to nodes: rather than computing a tensor product between every edge and its neighbour node, NEMP constructs an expressive equivariant structure via a single tensor product between the central node and a virtual summed node encoding its neighbours. This reduces the cost of the equivariant message-passing step from the number of neighbour pairs to the number of central atoms, achieving 1–2 orders of magnitude reduction in memory and compute over edge-equivariant baselines while matching or exceeding accuracy across molecules, extended systems, and universal-potential benchmarks. Published in Chemical Science (RSC, 2026).
Tags: equivariant, node-equivariant, efficient message passing, JAX
Category: Equivariant · Year: · Authors: Bhatia, Krejci, Botti, Rinke, Marques (Aalto / Friedrich Schiller University Jena / Ruhr University Bochum)
Foundation model for molecular infrared spectroscopy built on the MACE E(3)-equivariant message-passing architecture. The model consists of two parallel MACE networks — one for energies and forces, one for atomic dipole moments — trained on ~16 million molecular geometries with DFT energies, forces, and dipole moments from the QCML dataset (≈80 elements, organic molecules, inorganic species, and metal complexes). The MACE4IRmol variant (v2) wraps an ensemble of these networks for uncertainty quantification and delivers nuclear-quantum-effects-aware infrared spectra with DFT-level accuracy at a fraction of the cost. Released with model weights on Hugging Face and the QCML-derived AIMD trajectories on Zenodo.
Tags: equivariant, MACE family, IR spectroscopy, dipole moments, foundation model, uncertainty quantification
Category: Equivariant · Year: · Authors: Yang, Liu, Hu, Zhou, Shi, C. Liu, Tan, Li, Wang, Zhu, Chen, Thiemann, Zeni, Horton, Pinsler, Fowler, Zügner, Xie, Sun, Chen, Kong, Bai, Gunceler, Noé, Hao, Lu et al. (Microsoft Research)
Multi-task extension of the MatterSim foundation MLIP that predicts energies, forces, and stress jointly with electronic and tensorial materials properties — Bader charges, magnetic moments, Born effective charges, and full dielectric matrices — from a single shared atomistic backbone. Pretrained on 35M+ first-principles-labelled structures spanning 89 elements, temperatures up to 5000 K, and pressures up to 1000 GPa, then fine-tuned on the property-specific heads. Demonstrated on vibrational spectroscopy, ferroelectric switching, and electrochemical redox processes — workflows that conventional potential-energy-surface MLIPs cannot resolve out of the box.
License: MIT
Tags: transformer, foundation model, multi-task, Born effective charges, Bader charges, dielectric tensor
Category: Descriptor · Year: · Authors: Seko (Kyoto University)
Polynomial machine learning potential representing the atomic energy as a polynomial function of linearly independent polynomial invariants of the O(3) group built from local structural features. A systematically improvable linear/polynomial descriptor MLIP in the SNAP/MTP/ACE family, distributed via the pypolymlp toolkit and the curated Polynomial MLP Repository, and shipped to OpenKIM in March 2026 as a portable model driver with 837 elemental and alloy parameterizations for LAMMPS-scale simulations.
License: BSD-3-Clause
Tags: descriptor, linear, polynomial, O(3) invariants, pypolymlp, OpenKIM
Category: Descriptor · Year: · Authors: Li, Feng, Luo, Jiang, Zheng, Song, Lv, Butler, Liu, Xie, Xie, Ma (Jilin University / CALYPSO)
Attention-Coupled Neural Network potential: an expert MLIP architecture built from four modules — a local descriptor, an elemental embedding, a stack of optional multi-head attention modules, and an MLP-based fitting head. Stacking attention modules implicitly introduces an aggregative effect analogous to graph neural networks, extending the effective interaction range among atoms and enabling adaptive switching between network configurations based on the simulation task. Embedded in a self-optimizing CALYPSO crystal-structure-prediction workflow that iteratively refines the potential while exploring local minima of the potential energy surface, validated on Mg-Ca-H ternary and Be-P-N-O quaternary systems by exploring nearly 10 million configurations with substantial speedup over first-principles calculations.
Tags: descriptor, attention, self-optimizing, CSP, CALYPSO
Category: Descriptor · Year: · Authors: Wen, Han, Li, Chang, Chu, Chen (Beijing Institute of Technology)
General-purpose deep-potential neural network force field for energetic materials composed of C, H, N, and O. Built on the DeePMD-kit framework with a transfer-learning workflow that fine-tunes a pretrained NNP backbone on a small, targeted set of DFT energies and forces, achieving DFT-level accuracy across 20 different high-energy material (HEM) systems for structural, mechanical, and decomposition properties. Distributed as the EMFF-2025_V1.0.pb model for LAMMPS + DeepMD integration; suitable for MD simulations of HEM systems with 1–5000 atoms, delivering ~30× speedup over baseline LAMMPS via GPU parallel execution.
Tags: descriptor, Deep Potential, DeePMD, energetic materials, transfer learning
Paper: https://doi.org/10.1038/s41524-025-01809-w
Code: https://github.com/MingjieWen/General-NNP-model-for-C-H-N-O-Energetic-Materials
Category: Descriptor · Year: · Authors: Fan, W. Zhang, Z. Zhang, Xu, Shao, Dong (Bohai University)
Coarse-grained extension of the neuroevolution potential (NEP) framework that generates low-noise training data from the potential of mean force by constraining coarse-grained beads during atomistic simulations and accumulating time-averaged forces. Implemented within GPUMD, NEP-CG reaches training accuracy comparable to atomistic models trained on DFT data while running at hundreds to thousands of ns/day on a single consumer GPU. Demonstrated on liquid water (reproducing densities from 1 bar to 1 GPa with a virial correction for the correct equation of state) and an anisotropic C60 monolayer (capturing directional thermal conductivity). The companion NEP-AACG multiscale variant integrates all-atom and coarse-grained degrees of freedom in a single model, demonstrated for gold nanowire fracture at experimentally relevant strain rates.
Tags: descriptor, NEP family, coarse-grained, multiscale, GPUMD
Category: Equivariant · Year: · Authors: Gao, Yam, Mao, Chen, Chen, Hu (Univ. of Hong Kong / Hong Kong Quantum AI Lab / MattVerse)
Foundation machine learning potential that integrates explicit polarizable long-range electrostatics with an E(3)-equivariant message-passing graph neural network (built on e3nn-jax). Rather than predicting partial charges, ReaxNet employs a physically motivated polarizable charge-equilibration scheme that directly optimizes the electrostatic interaction energy and reproduces polarization responses under external electric fields — capturing long-range effects that elude standard cutoff-based message passing. Trained across the periodic table up to Pu and distributed as a JAX / JAX-MD implementation, it has been demonstrated on mechanical properties, ionic diffusivity in solid-state electrolytes, ferroelectric phase transitions, and reactive dynamics at electrode-electrolyte interfaces.
License: GPL-3.0
Tags: equivariant, polarisable, long-range-electrostatics, charge equilibration, JAX, e3nn-jax, foundation model
Category: Descriptor · Year: · Authors: X.Y. Li, J. Li, Y.N. Wang et al.
Domain-specific machine-learning interatomic potential for metallic materials covering 53 metallic elements — broad enough to span elemental metals, intermetallics, and multi-principal-element (high-entropy) alloys within a single model. Reaches DFT-level accuracy (energy MAE ≈ 12 meV/atom, force MAE ≈ 144 meV/Å) while staying efficient enough for large-scale molecular dynamics, and reproduces lattice parameters, elastic constants, and equations of state. Validated across four representative alloy problems: negative thermal expansion in orthorhombic Ti-Nb, the Elinvar effect in a Co25Ni25(TiZrHf)50 intermetallic, grain-boundary segregation and high-temperature deformation in the NbTaMoW refractory multi-principal-element alloy, and precipitation pathways.
Tags: descriptor, metals, alloys, high-entropy alloys, intermetallics, domain-specific
Category: Transformer · Year: · Authors: Eissler, Korjakow, Ganscha, Unke, Müller, Gugler (BIFOLD / TU Berlin / Google DeepMind)
Molecular-dynamics Edge Transformer: a deliberately minimal adaptation of an off-the-shelf Edge Transformer architecture to interatomic potentials, deployed with neither built-in equivariance nor energy conservation. Rather than encoding physical inductive biases into the network, MD-ET relies on a simple supervised pre-training scheme over ~30 million molecular structures from the QCML database and then fine-tunes for a small number of steps, reaching state-of-the-art accuracy on several molecular-dynamics benchmarks. The paper ("How simple can you go?") argues that, as in other ML domains, general-purpose transformer architectures paired with large-scale pre-training can rival specialised, physics-constrained networks for MD.
Tags: transformer, edge transformer, non-equivariant, off-the-shelf, large-scale pretraining
Category: Transformer · Year: · Authors: Kellner, Hansen, Bligaard, Jacobsen, Ceriotti (EPFL lab-cosmo / DTU)
Uncertainty-aware ensemble of universal interatomic potentials built on the Point Edge Transformer (PET) backbone. Rather than a single model, PET-UAFD ("universal DFT approximators") trains an ensemble across multiple electronic-structure references and calibrates it against experimental data — cohesive energies, atomization energies, lattice constants, and bulk moduli of simple materials and molecules — so that its predictions become as accurate against experiment as the best available electronic-structure reference while the ensemble spread reports prediction reliability. The companion PET-EXP protocol uses shallow ensembles and statistical reweighting to estimate uncertainty relative to experimental measurements at essentially no extra cost over a single conventional ML potential, accounting for the systematic error inherent in the underlying DFT functional.
Tags: transformer, PET, ensemble, uncertainty-quantification, experimental-calibration, lab-cosmo
Category: Equivariant · Year: · Authors: Brunken, Cormier, Walewski, Peltre, Chomet et al. (InstaDeep)
Mixture-of-Experts extension of Meta FAIR's eSEN architecture introduced in InstaDeep's mlip v2 framework. Routes through specialised expert kernels per chemical environment while contracting the routed kernels into a single dense kernel at inference, recovering the runtime cost of a standard single-head model. Built on the new e3j high-performance equivariant-operations backend (with dedicated CUDA and Pallas kernels for GPUs and TPUs) and shipped with pretrained checkpoints trained on a curated SPICE2 subset of OMol25. Integrates with ASE and JAX-MD wrappers and supports advanced simulation features such as NPT ensembles and nudged elastic band methods.
License: Apache-2.0
Tags: equivariant, mixture-of-experts, smooth PES, e3j backend, foundation model
Category: Equivariant · Year: · Authors: Pelletier, Bhat, Rivera, Wilson, Muhich (Arizona State University)
Transfer-PaiNN: a transfer-learning recipe that substantially improves the DFT data efficiency of GNN-MLIPs by pretraining a PaiNN backbone on large-scale (>100× the DFT set) classical force-field trajectories of the target system and then autotuning the weights on a small DFT dataset. The pretraining lets the network learn the broad shape of the potential energy surface from cheap classical sampling, with quantum accuracy supplied by the fine-tuning stage. Demonstrated on QM9 (gas-phase molecules) and condensed-phase liquid water, with up to ~25× MAE reduction in low-data regimes and improved energies, forces, density, and diffusivity predictions versus DFT-only training.
Tags: equivariant, transfer learning, data-efficient, PaiNN, autotuning
Category: Equivariant · Year: · Authors: Midgley, Lin, Moore, Della Pia, Antorán, Nilsson Lill, Eriksson, Faber, Tornberg, Broo, Csányi (AstraZeneca / Ångström AI / MPI Polymer Research / Cambridge)
Composite machine-learning interatomic potential targeting DFT-quality molecular crystal structure prediction (CSP) at a tiny fraction of DFT cost. Decomposes the total energy into intramolecular and intermolecular components: the intramolecular term is supplied by a MACE-POLAR model trained on OMol25, and the intermolecular term combines a MACE-POLAR contribution, an XDM-style long-range dispersion correction, and a learned Δ-model trained to reproduce B86bPBE-XDM intermolecular energies on ~50,000 molecular-crystal calculations. On the AstraZeneca CSP evaluation set (19 compounds) CSP-MACE-Å matches PBE-DFT-with-Neumann–Perrin accuracy, and on CSP blind-test compounds it approaches B86bPBE-XDM accuracy — making rigorous solid-form derisking tractable at scale.
Tags: equivariant, MACE, MACE-POLAR, crystal structure prediction, molecular crystals, delta-learning, XDM dispersion, long-range
Category: Equivariant · Year: · Authors: T. Li, W. Li, Peng, Xue, L. Zhang, D. Zhang, H. Wang (Peking Univ. / Tsinghua / AI for Science Institute / DP Technology / IAPCM)
Fourth-generation Deep Potential architecture that breaks with the prior invariant DPA-1/2/3 line by going SE(3)-equivariant via a new EMFA (Edge-conditioned, Multi-Focus, Attention) SO(2)-equivariant convolution. EMFA combines a low-rank edge–node SO(2)-equivariant product in an edge-local frame, a multi-focus design for message nonlinearity, and envelope-gated attention for message aggregation; a Lebedev-grid projection preserves SO(3)-equivariance in the nonlinearity to machine precision while reaching the same algebraic order of accuracy as latitude–longitude grids with substantially fewer sample points. Released in DPA4-Air (2.76 M params), DPA4-Plus (5.4 M), and DPA4-Pro variants — DPA4-Pro attains the best Combined Performance Score on the compliant Matbench Discovery leaderboard with ~31% fewer parameters than EquiformerV3+DeNS-MP, while DPA4-Air exceeds the 30.1 M-parameter eSEN-30M-MP baseline at 10.9× fewer parameters and 42.9× less training compute, redefining the SE(3)-equivariant foundation-MLIP Pareto frontier.
License: LGPL-3.0
Tags: equivariant, SO(2) convolution, EMFA, Lebedev grid, envelope-gated attention, DeePMD, foundation model