MLIP Hub
Interatomic Potential Explorer

Learn MLIPs

What are machine-learning interatomic potentials?

A practical guide to MLIP architectures, their physical constraints, and how to read the MLIP Hub map.

Explore the mapCompare models

1. What is an MLIP?

Machine-learning interatomic potentials, or MLIPs, use machine learning to approximate the energy and forces of atomistic systems. They are designed to make molecular dynamics, structure relaxation, materials screening, and related simulations much faster than repeatedly solving the electronic-structure problem from scratch.

An atomistic simulation needs a rule for computing how atoms interact. In first-principles simulations, that rule comes from electronic-structure calculations such as density functional theory. In an MLIP, the rule is learned from reference data.

A typical MLIP takes an atomic structure as input:

  • atomic numbers,
  • positions,
  • periodic cell information when relevant,
  • and sometimes total charge, spin, or other conditioning variables.

It then predicts one or more physical quantities, most commonly:

  • total energy,
  • atomic forces,
  • stress or virial,
  • sometimes charge, dipole, magnetic moment, or polarizability.

Many MLIPs predict a scalar energy and compute forces as derivatives of that energy. Other models may predict forces directly. This distinction matters because derivative-based forces are energy-conservative by construction, while direct-force models may trade strict conservatism for speed or flexibility.

2. What makes a good MLIP architecture?

MLIP architectures are shaped by physical symmetries and computational trade-offs.

Symmetry

A physically sensible MLIP should respect basic symmetries:

  • Translation invariance: shifting the whole structure should not change the energy.
  • Permutation symmetry: swapping identical atoms should not change the energy.
  • Rotation invariance for scalar outputs: rotating the structure should not change the total energy.
  • Rotation equivariance for vector outputs: if the structure rotates, predicted vector quantities such as forces should rotate in the same way.

Locality and long-range effects

Most MLIPs use local neighborhoods: each atom interacts with atoms inside a cutoff radius. This is efficient and often accurate for short-range bonding. Long-range electrostatics, polarization, charge transfer, and magnetic effects may require special treatment.

Accuracy, speed, and data efficiency

Architectures differ in how much physics they build in. More structured models can be data-efficient and accurate, but may be more expensive. Simpler or less constrained models can be faster, especially for large simulations, but may require more data or careful validation.

3. Main MLIP architecture families

Use these as a reading guide for the map. Many real models combine ideas from multiple families.

Descriptor-based potentials

Core idea. Convert each atom's neighborhood into a fixed numerical descriptor, then use a regression model or neural network to predict atomic energy contributions.

How it works

  1. Build local atomic environments.
  2. Encode each environment with symmetry-preserving descriptors.
  3. Feed descriptors into a regressor or neural network.
  4. Sum atomic contributions into total energy.

Representative examples

  • Behler–Parrinello NNs
  • ANI
  • GAP / SOAP
  • SNAP
  • MTP
  • ACE
  • NEP

Strengths

  • Often fast at inference.
  • Robust and practical for production molecular dynamics.
  • Descriptor design can encode useful physical structure.

Limitations

  • Descriptor choices strongly affect performance.
  • High body-order descriptors can become expensive.
  • Transferability depends on training data and descriptor expressivity.

Invariant graph neural networks

Core idea. Represent atoms as graph nodes and pass scalar messages through neighbor edges, keeping internal features invariant under rotation.

How it works

  1. Atoms become graph nodes.
  2. Distances and angular features become edge features.
  3. Each atom updates its representation by aggregating neighbor messages.
  4. A readout predicts energy and other scalar quantities.

Representative examples

  • SchNet
  • DimeNet
  • GemNet-style models

Strengths

  • Natural fit for atomistic systems.
  • Learns representations rather than relying only on fixed descriptors.
  • Often easier to scale than highly structured tensor models.

Limitations

  • Purely invariant features may be less efficient for vector or tensor properties.
  • Geometry quality depends on careful angular and directional feature design.

Equivariant graph neural networks

Core idea. Carry features that transform predictably under rotations, so geometry, directions, and tensor quantities can be represented natively.

How it works

  1. Construct an atomistic graph.
  2. Use directional geometric features such as spherical harmonics or tensor products.
  3. Pass messages that preserve E(3), SE(3), or related equivariance.
  4. Predict invariant energies and equivariant vector or tensor outputs.

Representative examples

  • Tensor Field Networks
  • NequIP
  • Allegro
  • MACE
  • eSEN
  • Equiformer-style models

Strengths

  • Strong physical inductive bias.
  • Often highly data-efficient.
  • Especially useful for forces, local geometry, and tensorial properties.

Limitations

  • Can be computationally heavier.
  • Implementation complexity is higher.
  • Very large-scale MD may need local or optimized variants.

Attention and transformer-style MLIPs

Core idea. Use attention mechanisms to let atoms or local environments weigh the importance of other atoms, edges, or learned features.

How it works

  1. Build atom, edge, or environment tokens.
  2. Compute attention scores over local or sparse neighborhoods.
  3. Mix features according to learned relevance.
  4. Combine attention with invariant or equivariant geometric features.

Representative examples

  • SE(3)-Transformer
  • Equiformer
  • PET
  • Orb-style graph models
  • UMA-style foundation models

Strengths

  • Flexible information routing.
  • Works well with large pretraining datasets.
  • Can be combined with equivariance or relaxed symmetry assumptions.

Limitations

  • Attention can be expensive without locality or sparsity.
  • The transformer label alone does not specify physical constraints.
  • Some models intentionally relax strict equivariance for speed.

Foundation MLIPs

Core idea. Broadly pretrained atomistic models designed for direct use, transfer learning, or fine-tuning across many materials or molecular domains.

How it works

  1. Pretrain on many structures, chemistries, and configurations.
  2. Learn a general atomistic representation.
  3. Apply zero-shot, use as a starting point, or fine-tune.
  4. Validate carefully for the target chemistry, phase, and conditions.

Representative examples

  • MACE-MP-style models
  • CHGNet
  • MatterSim
  • Orb
  • SevenNet
  • UMA

Strengths

  • Broad initial coverage.
  • Useful starting point for screening and exploratory simulations.
  • Can reduce the amount of task-specific training data needed.

Limitations

  • “Universal” does not mean universally accurate.
  • Coverage depends on training data.
  • Target-domain validation remains necessary.

4. Architecture taxonomy chart

The chart below is the page’s anchor visual. It is a practical reading guide for MLIP Hub, not a strict ontology or ranking.

5. How to read the MLIP Hub map

MLIP Hub shows model families as zones, models as nodes, and curated relationships as edges.

Nodes

Each node is a specific model or architecture entry. A node card may include name, year, category, originating lab or authors, code link, paper link, training data, predicted properties, framework support, license, maintenance status, charge/spin support, and element coverage.

Edges

An edge indicates a curated conceptual relationship. It may mean that one model influenced another, extended a prior design, adapted an architecture, or belongs to a related lineage.

Zones

Zones group models into broad architecture families such as descriptor, invariant, equivariant, transformer, or foundation-style MLIPs. Some models naturally sit between categories.

An edge is not necessarily code inheritance, citation count, or benchmark superiority. It is a curator-reviewed lineage or conceptual relationship.

See the live map at Explore, the full sortable list at Table, or compare any two side by side at Compare.

6. Choosing what to compare

This section is a checklist, not a recommendation. We do not name a best model. Use it to figure out which metadata to read on each model card.

If you care about molecular dynamics

  • Force support.
  • Energy conservation assumptions (derivative vs direct forces).
  • Speed and memory.
  • MD engine integration.
  • Stability over long trajectories.
  • Validation at your target temperature and phase.

If you care about periodic materials

  • Stress prediction.
  • Periodic boundary support.
  • Element coverage.
  • Training data relevance.
  • Support for ASE, LAMMPS, OpenKIM, or related workflows.

If you care about charged, spin, or polar systems

  • Whether the model supports total charge.
  • Whether it supports spin or magnetic moments.
  • Whether it includes long-range electrostatics or polarization.
  • Whether those capabilities were trained and validated for your chemistry.

If you care about fine-tuning

  • License.
  • Availability of pretrained weights.
  • Training code.
  • Target-domain data requirements.
  • Examples for transfer learning or fine-tuning.

7. Glossary

MLIP
A machine-learning interatomic potential: a learned approximation to atomistic energies, forces, and related quantities.
Potential energy surface
The function mapping atomic positions and species to energy.
Forces
The negative gradient of energy with respect to atomic positions.
Stress / virial
A quantity related to how energy changes with cell deformation, important for periodic materials.
Descriptor
A numerical representation of an atom's local environment.
Invariant
A quantity that does not change under a transformation, such as energy under rotation.
Equivariant
A quantity that transforms in a predictable way under a transformation, such as forces rotating when the structure rotates.
Message passing
A graph neural network operation where atoms update their features by receiving information from neighboring atoms.
Cutoff radius
The distance within which atoms are considered neighbors.
Foundation MLIP
A broadly pretrained atomistic model intended to cover many chemistries or materials and often used directly or fine-tuned.
Long-range interactions
Interactions such as electrostatics or polarization that may extend beyond a short local cutoff.
Charge-aware model
A model that can condition predictions on total or atomic charge.
Spin-aware model
A model that can condition predictions on spin multiplicity, magnetic moments, or related variables.

8. Further reading

A curated reading list. Follow each model card’s paperUrl for canonical citations.

General MLIP reviews

  • Unke et al., “Machine Learning Force Fields,” Chemical Reviews, 2021.
  • Behler, “Perspective: Machine learning potentials for atomistic simulations,” Journal of Chemical Physics, 2016.
  • Deringer, Caro, and Csányi, “Machine learning interatomic potentials as emerging tools for materials science,” Advanced Materials, 2019.

Descriptor and kernel models

  • Behler and Parrinello, high-dimensional neural network potentials.
  • Bartók, Payne, Kondor, and Csányi, Gaussian Approximation Potentials.
  • SOAP descriptor papers by Bartók and coauthors.
  • Thompson et al., SNAP.
  • Shapeev, Moment Tensor Potentials.
  • Drautz, Atomic Cluster Expansion.
  • ANI papers by Smith, Isayev, and Roitberg.
  • NEP papers by Fan and coauthors.

Graph neural network MLIPs

  • SchNet by Schütt and coauthors.
  • DimeNet by Klicpera and coauthors.
  • GemNet / GemNet-OC by Gasteiger and coauthors.

Equivariant MLIPs

  • Tensor Field Networks by Thomas and coauthors.
  • NequIP by Batzner and coauthors.
  • Allegro by Musaelian and coauthors.
  • MACE by Batatia and coauthors.
  • eSEN / related smooth equivariant models.

Attention and transformer-style MLIPs

  • SE(3)-Transformer by Fuchs and coauthors.
  • Equiformer and EquiformerV2 by Liao, Smidt, and coauthors.
  • PET / PET-MAD by Pozdnyakov, Ceriotti, and coauthors.
  • Orb / UMA / related foundation-model papers.