Warning

This repository is a successor of the PET-MAD repository, which is now deprecated. The package has been renamed to UPET to reflect the broader scope of the models and functionalities provided, that go beyond the original PET-MAD model. Please use the version 1.4.4 of PET-MAD package if you want to use the old API. The older version of the README file with documentation is avaiable here. The migration guide from PET-MAD to UPET is available here.

Note

Are you here to try our Matbench model? Here's all you need. Don't be scared by the parameter count: you'll see that our model is much faster than you think. This model is excellent for convex hull energies, geometry optimization and phonons, but we highly recommend the lighter and more universal PET-MAD for molecular dynamics!

from upet.calculator import UPETCalculator
calculator = UPETCalculator(model="pet-oam-xl", version="1.0.0", device="cuda")

UPET: Universal Models for Advanced Atomistic Simulations

This repository contains UPET models - universal interatomic potentials for advanced materials modeling across the periodic table. These models are based on the Point Edge Transformer (PET) architecture, trained on various popular materials datasets, and are capable of predicting energies and forces in complex atomistic simulations.

In addition, it contains PET-MAD-DOS - a universal model for predicting the density of states (DOS) of materials, as well as their Fermi levels and bandgaps. PET-MAD-DOS is using a slightly modified PET architecture, and the MAD dataset.

Key Features

• Universality: UPET models are generally-applicable, and can be used for predicting energies and forces, as well as the density of states, Fermi levels, and bandgaps for a wide range of materials and molecules.
• Accuracy: UPET models achieve high accuracy in various types of atomistic simulations of organic and inorganic systems, comparable with system-specific models, while being fast and efficient.
• Efficiency: UPET models are highly computationally efficient and have low memory usage, what makes them suitable for large-scale simulations.
• Infrastructure: Various MD engines are available for diverse research and application needs.
• HPC Compatibility: Efficient in HPC environments for extensive simulations.

Table of Contents

1. Installation
2. Pre-trained Models
3. Interfaces for Atomistic Simulations
4. Usage
   • ASE Interface
     • Basic usage
     • Non-conservative (direct) forces and stresses prediction
   • Evaluating UPET models on a dataset
   • Running UPET models with LAMMPS
   • Uncertainty Quantification
   • Rotational Averaging
   • Running UPET models with empirical dispersion corrections
   • Calculating the DOS, Fermi levels, and bandgaps
   • Dataset visualization with the PET-MAD featurizer
5. Examples
6. Fine-tuning
7. Further Documentation
8. FAQs
9. Known Issues
10. Citing UPET Models

Installation

You can install UPET using pip:

pip install upet

Or directly from the GitHub repository:

pip install git+https://github.com/lab-cosmo/upet.git

Pre-trained Models

Currently, we provide the following pre-trained models:

Name	Level of theory	Available sizes	To be used for	Training set
PET-MAD	PBEsol	S	materials and molecules	MAD
PET-OMAD	PBEsol	XS, S, L	materials and molecules	OMat -> MAD
PET-OAM	PBE (Materials Project)	L, XL	materials	OMat -> sAlex+MPtrj
PET-OMat	PBE	XS, S, M, L, XL	materials	OMat
PET-OMATPES	r2SCAN	L	materials	OMat -> MATPES
PET-SPICE	ωB97M-D3	S, L	molecules	SPICE

We recommend using the PET-MAD model for molecular dynamics simulations of materials, PET-OAM models for materials discovery tasks (convex hull energies, geometry optimization, phonons, etc), and PET-SPICE for accurate and fast simulations of biomolecules. PET-OMAD models are more accurate and potentially faster than PET-MAD, but they were not tested as extensively yet. PET-OMATPES can be a good choice in case the accuracy of the PBE functionals are not sufficient for your applications.

All the checkpoints are available on the HuggingFace repository.

Interfaces for Atomistic Simulations

UPET integrates with the following atomistic simulation engines:

• Atomic Simulation Environment (ASE)
• LAMMPS (including the KOKKOS support)
• i-PI
• OpenMM (coming soon)
• GROMACS (coming soon)

Usage

ASE Interface

Basic usage

In order to perform a simple evaluation of the UPET models on a desired structure, you can use the UPET calculator compatible with the Atomic Simulation Environment (ASE). Model name can be obtained from the table above by combining the model name and the size, e.g., pet-mad-s, pet-omat-l, etc.

from upet.calculator import UPETCalculator
from ase.build import bulk

atoms = bulk("Si", cubic=True, a=5.43, crystalstructure="diamond")
calculator = UPETCalculator(model="pet-mad-s", version="1.0.2", device="cpu")
atoms.calc = calculator
energy = atoms.get_potential_energy()
forces = atoms.get_forces()

These ASE methods are ideal for single-structure evaluations, but they are inefficient for the evaluation on a large number of pre-defined structures. To perform efficient evaluation in that case, read here.

Non-conservative (direct) forces and stresses prediction

UPET models also support the direct prediction of forces and stresses. In that case, the forces and stresses are predicted as separate targets along with the energy target, i.e. not computed as derivatives of the energy using the PyTorch automatic differentiation. This approach typically leads to 2-3x speedup in the evaluation time, since backward pass is disabled. However, as discussed in this preprint, the non-conservative forces and stresses require additional care to avoid instabilities during the molecular dynamics simulations.

To use the non-conservative forces and stresses, you need to set the non_conservative parameter to True when initializing the UPETCalculator class.

from upet.calculator import UPETCalculator
from ase.build import bulk

atoms = bulk("Si", cubic=True, a=5.43, crystalstructure="diamond")
calculator = UPETCalculator(model="pet-mad-s", version="1.1.0", device="cpu", non_conservative=True)
atoms.calc = calculator
energy = atoms.get_potential_energy() # energy is computed as usual
forces = atoms.get_forces() # forces now are predicted as a separate target
stresses = atoms.get_stress() # stresses now are predicted as a separate target

More details on how to make the direct forces MD simulations reliable are provided in the Atomistic Cookbook.

Evaluating UPET models on a dataset

Efficient evaluation of UPET models on a desired dataset is also available from the command line via metatrain, which is installed as a dependency of UPET. To evaluate the model, you first need to fetch the UPET model from the HuggingFace repository:

mtt export https://huggingface.co/lab-cosmo/upet/resolve/main/models/pet-mad-s-v1.0.2.ckpt -o model.pt

Alternatively, you can fetch and save the model using the UPET Python API:

import upet

# Saving the latest version of UPET to a TorchScript file
upet.save_upet(
    model="pet-mad",
    size="s",
    version="1.0.2",
    output="model.pt",
)

Both these commands will download the model and convert it to TorchScript format. Next, you need to create the options.yaml file and specify the dataset you want to evaluate the model on (where the dataset is stored in extxyz format):

systems: your-test-dataset.xyz
targets:
  energy:
    key: "energy"
    unit: "eV"

Then, you can use the mtt eval command to evaluate the model on a dataset:

mtt eval model.pt options.yaml --batch-size=16 --output=predictions.xyz

This will create a file called predictions.xyz with the predicted energies and forces for each structure in the dataset. More details on how to use metatrain can be found in the Metatrain documentation.

Running UPET models with LAMMPS

1. Install LAMMPS with metatomic support

To use UPET with LAMMPS, follow the instructions here to install lammps-metatomic. We recomend you also use conda to install prebuilt lammps binaries.

2. Run LAMMPS with UPET

2.1. CPU version

Fetch the UPET checkpoint from the HuggingFace repository:

mtt export https://huggingface.co/lab-cosmo/upet/resolve/main/models/pet-mad-s-v1.0.2.ckpt -o model.pt

This will download the model and convert it to TorchScript format compatible with LAMMPS, using the metatomic and metatrain libraries, which UPET is based on.

Other pre-trained UPET models can be prepared in the same way, e.g.,

mtt export https://huggingface.co/lab-cosmo/upet/resolve/main/models/pet-omat-xs-v1.0.0.ckpt -o model.pt
mtt export https://huggingface.co/lab-cosmo/upet/resolve/main/models/pet-omatpes-l-v0.1.0.ckpt -o model.pt

Prepare a lammps input file using pair_style metatomic and defining the mapping from LAMMPS types in the data file to elements UPET can handle using pair_coeff syntax. Here we indicate that lammps atom type 1 is Silicon (atomic number 14).

units metal
atom_style atomic

read_data silicon.data

pair_style metatomic model.pt device cpu # Change device to 'cuda' evaluate UPET on GPU
pair_coeff * * 14

neighbor 2.0 bin
timestep 0.001

dump myDump all xyz 10 trajectory.xyz
dump_modify myDump element Si

thermo_style multi
thermo 1

velocity all create 300 87287 mom yes rot yes

fix 1 all nvt temp 300 300 0.10

run 100

Create the silicon.data data file for a silicon system.

# LAMMPS data file for Silicon unit cell
8 atoms
1 atom types

0.0  5.43  xlo xhi
0.0  5.43  ylo yhi
0.0  5.43  zlo zhi

Masses

1  28.084999992775295 # Si

Atoms # atomic

1   1   0   0   0
2   1   1.3575   1.3575   1.3575
3   1   0   2.715   2.715
4   1   1.3575   4.0725   4.0725
5   1   2.715   0   2.715
6   1   4.0725   1.3575   4.0725
7   1   2.715   2.715   0
8   1   4.0725   4.0725   1.3575

lmp -in lammps.in  # For serial version
mpirun -np 1 lmp -in lammps.in  # For MPI version

2.2. KOKKOS-enabled GPU version

Running LAMMPS with KOKKOS and GPU support is similar to the CPU version, but you need to change the lammps.in slightly and run lmp binary with a few additional flags.

The updated lammps.in file looks like this:

package kokkos newton on neigh half

units metal
atom_style atomic/kk

read_data silicon.data

pair_style metatomic/kk model.pt # This will use the same device as the kokkos simulation
pair_coeff * * 14

neighbor 2.0 bin
timestep 0.001

dump myDump all xyz 10 trajectory.xyz
dump_modify myDump element Si

thermo_style multi
thermo 1

velocity all create 300 87287 mom yes rot yes

fix 1 all nvt temp 300 300 0.10

run_style verlet/kk
run 100

The silicon.data file remains the same.

To run the KOKKOS-enabled version of LAMMPS, you need to run

lmp -in lammps.in -k on g 1 -sf kk # For serial version
mpirun -np 1 lmp -in lammps.in -k on g 1 -sf kk # For MPI version

Here, the -k on g 1 -sf kk flags are used to activate the KOKKOS subroutines. Specifically g 1 is used to specify, how many GPUs are the simulation is parallelized over, so if running the large systems on two or more GPUs, this number should be adjusted accordingly.

Important Notes

• For CPU calculations, use a single MPI task unless simulating large systems (30+ Å box size). Multi-threading can be enabled via:

  export OMP_NUM_THREADS=4

• For GPU calculations, use one MPI task per GPU.

Uncertainty Quantification

UPET models can also be used to calculate the uncertainty of the energy prediction. This feature is particularly important if you are interested in probing the model on the data that is substantially different from the training data. Another important use case is a propagation of the uncertainty of the energy prediction to other observables, like phase transition temperatures, diffusion coefficients, etc.

To evaluate the uncertainty of the energy prediction, or to get an ensemble of energy predictions, you can use the get_energy_uncertainty and get_energy_ensemble methods of the UPETCalculator class:

from upet.calculator import UPETCalculator
from ase.build import bulk

atoms = bulk("Si", cubic=True, a=5.43, crystalstructure="diamond")
calculator = UPETCalculator(model="pet-mad-s", version="1.0.2", device="cpu", calculate_uncertainty=True, calculate_ensemble=True)
atoms.calc = calculator
energy = atoms.get_potential_energy()

energy_uncertainty = calculator.get_energy_uncertainty(atoms, per_atom=False)
energy_ensemble = calculator.get_energy_ensemble(atoms, per_atom=False)

Please note that the uncertainty quantification and ensemble prediction accepts the per_atom flag, which indicates whether the uncertainty/ensemble should be computed per atom or for the whole system. More details on the uncertainty quantification and shallow ensemble method can be found in this and this papers.

Rotational Averaging

By design, UPET models are not exactly equivariant w.r.t. rotations and inversions. Although the equivariance error is typically much smaller than the overall model error, in some cases (like geometry optimizations and phonon calculations of highly symmetrical structures) it may be beneficial to enforce additional rotational averaging to improve the stability of the calculation. This can be done by setting the rotational_average_order parameter when initializing the UPETCalculator class:

from upet.calculator import UPETCalculator
from ase.build import bulk

atoms = bulk("Si", cubic=True, a=5.43, crystalstructure="diamond")
calculator = UPETCalculator(model="pet-mad-s", version="1.0.2", device="cpu", rotational_average_order=3)
atoms.calc = calculator
energy = atoms.get_potential_energy()
forces = atoms.get_forces()
stresses = atoms.get_stress()

In this case, predictions will be averaged over a quadrature of the O(3) group based on a Lebedev grid of the specified order (here 3). Higher orders lead to more accurate equivariance, but also increase the computational cost.

By default, all the transformed structures are evaluated in a single batch, which may lead to high memory usage for large systems. If you want to reduce the memory usage, you can set the rotational_average_batch_size parameter to a smaller value (eg. 8), which will evaluate the transformed structures in smaller batches:

from upet.calculator import UPETCalculator
calculator = UPETCalculator(model="pet-mad-s", version="1.0.2", device="cpu", rotational_average_order=3, rotational_average_batch_size=8)

Finally, the rotational averaging error statistics are stored in the results dictionary of the calculator after the energy/forces/stresses are computed:

energy_rot_std = calculator.results['energy_rot_std']
forces_rot_std = calculator.results['forces_rot_std']
stresses_rot_std = calculator.results['stresses_rot_std']

Running UPET models with empirical dispersion corrections

In ASE:

You can combine the UPET calculator with the torch based implementation of the D3 dispersion correction of pfnet-research - torch-dftd:

Within the UPET environment you can install torch-dftd via:

pip install torch-dftd

Then you can use the D3Calculator class to combine the two calculators:

from torch_dftd.torch_dftd3_calculator import TorchDFTD3Calculator
from upet.calculator import UPETCalculator
from ase.calculators.mixing import SumCalculator

device = "cuda" if torch.cuda.is_available() else "cpu"

calc_MAD = UPETCalculator(model="pet-mad-s", version="1.0.2", device=device)
dft_d3 = TorchDFTD3Calculator(device=device, xc="pbesol", damping="bj")

combined_calc = SumCalculator([calc_MAD, dft_d3])

# assign the calculator to the atoms object
atoms.calc = combined_calc

Calculating the DOS, Fermi levels, and bandgaps

UPET package also allows the use of the PET-MAD-DOS model to predict electronic density of states of materials, as well as their Fermi levels and bandgaps. The PET-MAD-DOS model is also available in the ASE interface.

from upet.calculator import PETMADDOSCalculator

atoms = bulk("Si", cubic=True, a=5.43, crystalstructure="diamond")
pet_mad_dos_calculator = PETMADDOSCalculator(version="latest", device="cpu")

energies, dos = pet_mad_dos_calculator.calculate_dos(atoms)

Predicting the densities of states for every atom in the crystal, or a list of atoms, is also possible:

# Calculating the DOS for every atom in the crystal
energies, dos_per_atom = pet_mad_dos_calculator.calculate_dos(atoms, per_atom=True)

# Calculating the DOS for a list of atoms
atoms_1 = bulk("Si", cubic=True, a=5.43, crystalstructure="diamond")
atoms_2 = bulk("C", cubic=True, a=3.55, crystalstructure="diamond")

energies, dos = pet_mad_dos_calculator.calculate_dos([atoms_1, atoms_2], per_atom=False)

Finally, you can use the calculate_bandgap and calculate_efermi methods to predict the bandgap and Fermi level for the crystal:

bandgap = pet_mad_dos_calculator.calculate_bandgap(atoms)
fermi_level = pet_mad_dos_calculator.calculate_efermi(atoms)

You can also re-use the DOS calculated earlier:

bandgap = pet_mad_dos_calculator.calculate_bandgap(atoms, dos=dos)
fermi_level = pet_mad_dos_calculator.calculate_efermi(atoms, dos=dos)

This option is also available for a list of ase.Atoms objects:

bandgaps = pet_mad_dos_calculator.calculate_bandgap([atoms_1, atoms_2], dos=dos)
fermi_levels = pet_mad_dos_calculator.calculate_efermi([atoms_1, atoms_2], dos=dos)

Dataset visualization with the PET-MAD featurizer

You can use the last-layer features of the PET-MAD model together with a pre-trained sketch-map dimensionality reduction to obtain 2D and 3D representations of a dataset, e.g. to identify structural or chemical motifs. This can be used as a stand-alone feature builder, or combined with the chemiscope viewer to generate an interactive visualization.

import ase.io
import chemiscope
from upet.explore import PETMADFeaturizer

featurizer = PETMADFeaturizer(version="latest")

# Load structures
frames = ase.io.read("dataset.xyz", ":")

# You can just compute features
features = featurizer(frames, None)

# Or create an interactive visualization in a Jupyter notebook
chemiscope.explore(
    frames,
    featurize=featurizer
)

Examples

More examples for ASE, i-PI, and LAMMPS are available in the Atomistic Cookbook.

Fine-tuning

General Information

UPET models can be fine-tuned using the Metatrain library. At the moment, we recommend fine-tuning from our OMat models, because they are pre-trained on a very large dataset and they come in all sizes (from XS to XL, allowing you to choose a good trade-off for your application).

Heads Selection

It's important to note, that by default the UPETCalculator class uses the default energy and non-conservative forces/stresses heads provided with the pre-trained models. If you fine-tune the model and create a new head for your energy target, you should explicitly select the corresponding energy variant on runtime (same for non-conservative forces/stresses). Let's consider an example, where you fine-tune the energy head and call it "energy/finetune" in the options.yaml file, while running mtt train command.

ASE Interface

In ASE, running the model with a variant selection can be done by loading your trained checkpoint and initializing the UPETCalculator class with the variants parameter:

from upet.calculator import UPETCalculator

# For the new energy head called "energy/finetune"
calc = UPETCalculator(checkpoint_name="finetuned.ckpt", variants={'energy': 'finetune'})

Same applies to non-conservative forces and stresses, if you created new heads for them during fine-tuning.

Metatrain Interface

Similarly to ASE calculator, you can select the new head for evaluation with metatrain while running mtt eval command by specifying the head in the options.yaml file:

systems: your-test-dataset.xyz
targets:
  energy/finetune:
    key: "energy"
    unit: "eV"

LAMMPS Interface

In LAMMPS, you can select the new head by specifying the variant/energy parameter in the pair_style metatomic command:

read_data silicon.data

pair_style metatomic model.pt variant/energy finetune
pair_coeff * * 14

Further Documentation

Additional documentation can be found in the metatensor, metatomic and metatrain repositories.

• Training a model
• Fine-tuning
• LAMMPS interface
• i-PI interface

FAQs

What model should I use for my application?

• For molecular dynamics simulations, we recommend using the PET-MAD model. Alternatively, you can use the PET-OMAD models, which are more accurate and potentially faster, but they were not tested as extensively yet.
• For materials discovery tasks (convex hull energies, geometry optimization, phonons, etc), we recommend using the PET-OAM models.
• For accurate and fast simulations of biomolecules, we recommend using the PET-SPICE models.
• In case the accuracy of the PBE functionals is not sufficient for your application, you can try the PET-OMATPES model for simulations of materials.
• If you want to fine-tune your own model, we recommend starting from the PET-OMAT checkpoints, and select an appropriate size (from XS to XL) for your needs.
• In any case, we recommend starting from the smaller models (XS or S) to benchmark your application, and then scaling up to larger models if you need more accuracy.

The model is slow for my application. What should I do?

• Make sure you run it on a GPU
• Use an S or XS model
• Simulate with LAMMPS (Kokkos-GPU version)
• Use non-conservative forces and stresses, preferably with multiple time stepping. Check out this example for details.
• Still too slow? Check out FlashMD for a further 30x boost.

My MD ran out of memory. How do I fix that?

• Reduce the model size (XS models are the least memory-intensive)
• Reduce the structure size
• Try to use LAMMPS (Kokkos-GPU version) and run with multiple MPI tasks to enable domain decomposition
• As a last resort, use non-conservative forces and stresses
• If you hit a weird bug when running more than 65535 atoms on GPU, this is not an out-of-memory bug, but a pytorch bug. You can fix it by adding torch.backends.cuda.enable_mem_efficient_sdp(False) (after importing torch) near the top of your file.

The model is not fully equivariant. Should I worry?

Although our models are unconstrained, they are explicitly trained for equivariance, and the equivariance error is, in the vast majority of cases, one to two orders of magnitude smaller than the machine-learning error with respect to the target electronic structure method. Hence:

• Read this paper which shows that the impact of non-equivariance on observables is often negligible. Proceed to the next two points only if you believe that you're seeing effects due to non-equivariance.
• For MD, activate random frame averaging (we are working on a tutorial)
• For geometry optimization, use a symmetrized calculator (see rotational_average_order parameter in the ASE calculator)

The XL models are huge!

There are two aspects to this:

• The number of parameters is large, but these parameters are used in a very sparse way and the evaluation cost is comparable to, and often lower than, that of other large models in the field.
• The listed cutoff radius may be large, but the cutoff strategy is adaptive, meaning that the model prunes the neighbor list internally. The effective cutoff for the vast majority of atomic environments in materials ends up being between 4 and 7 A in practice.

If you are fine-tuning our models, please also see the metatrain FAQs

Known Issues

Simulation blows up with lammps-metatomic 2025.9.10.mta2

While running upet models with the version above, we observe that simulations blow up. This is most likely a bug introduced in a recent PR in lammps-metatomic. For now, we recommend using lammps-metatomic==2025.9.10.mta1.

Citing UPET Models

If you use any of the UPET models in your research, please cite the appropriate article:

@misc{pushing-unconstrained-2026,
      title={Pushing the limits of unconstrained machine-learned interatomic potentials}, 
      author={Filippo Bigi and Paolo Pegolo and Arslan Mazitov and Michele Ceriotti},
      year={2026},
      eprint={2601.16195},
      archivePrefix={arXiv},
      primaryClass={physics.chem-ph},
      url={https://arxiv.org/abs/2601.16195}, 
}
@misc{PET-MAD-2025,
      title={PET-MAD as a lightweight universal interatomic potential for advanced materials modeling},
      author={Mazitov, Arslan and Bigi, Filippo and Kellner, Matthias and Pegolo, Paolo and Tisi, Davide and Fraux, Guillaume and Pozdnyakov, Sergey and Loche, Philip and Ceriotti, Michele},
      journal={Nature Communications},
      volume={16},
      number={1},
      pages={10653},
      year={2025},
      url={https://doi.org/10.1038/s41467-025-65662-7},
}
@misc{PET-MAD-DOS-2025,
      title={A universal machine learning model for the electronic density of states}, 
      author={Wei Bin How and Pol Febrer and Sanggyu Chong and Arslan Mazitov and Filippo Bigi and Matthias Kellner and Sergey Pozdnyakov and Michele Ceriotti},
      year={2025},
      eprint={2508.17418},
      archivePrefix={arXiv},
      primaryClass={physics.chem-ph},
      url={https://arxiv.org/abs/2508.17418}, 
}

For a general citation for the PET architecture, you can use

@misc{PET-ECSE-2023,
  title = {Smooth, Exact Rotational Symmetrization for Deep Learning on Point Clouds},
  journal = {Advances in {{Neural Information Processing Systems}}},
  author = {Pozdnyakov, Sergey and Ceriotti, Michele},
  year = 2023,
  volume = {36},
  pages = {79469--79501},
}