Positions

Positions are differences between atomic positions at two different times. They can be used to predict the next configuration in molecular dynamics (see, e.g., https://arxiv.org/pdf/2505.19350).

In metatomic models, they are associated with the "positions" key in the model outputs, and must adhere to the following metadata schema:

Metadata for positions

Metadata	Names	Description
keys	"_"	the keys must have a single dimension named "_", with a single entry set to 0. Positions are always a metatensor.torch.TensorMap with a single block.
samples	["system", "atom"]	the samples must be named ["system", "atom"], since positions are always per-atom. "system" must range from 0 to the number of systems given as an input to the model. "atom" must range between 0 and the number of atoms/particles in the corresponding system. If selected_atoms is provided, then only the selected atoms for each system should be part of the samples.
components	"xyz"	positions must have a single component dimension named "xyz", with three entries set to 0, 1, and 2. The positions are always 3D vectors, and the order of the components is x, y, z.
properties	"positions"	positions must have a single property dimension named "positions", with a single entry set to 0.

At the moment, positions are not integrated into any simulation engines.

Momenta

The momentum of a particle is a vector defined as its mass times its velocity. Predictions of momenta can be used, for example, to predict a future step in molecular dynamics (see, e.g., https://arxiv.org/pdf/2505.19350).

In metatomic models, they are associated with the "momenta" key in the model outputs, and must adhere to the following metadata schema:

Metadata for momenta

Metadata	Names	Description
keys	"_"	the keys must have a single dimension named "_", with a single entry set to 0. Momenta are always a metatensor.torch.TensorMap with a single block.
samples	["system", "atom"]	the samples must be named ["system", "atom"], since momenta are always per-atom. "system" must range from 0 to the number of systems given as an input to the model. "atom" must range between 0 and the number of atoms/particles in the corresponding system. If selected_atoms is provided, then only the selected atoms for each system should be part of the samples.
components	"xyz"	momenta must have a single component dimension named "xyz", with three entries set to 0, 1, and 2. The momenta are always 3D vectors, and the order of the components is x, y, z.
properties	"momenta"	momenta must have a single property dimension named "momenta", with a single entry set to 0.

At the moment, momenta are not integrated into any simulation engines.