Momentum

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 "momentum" or "momentum/<variant>" name (see Variants), and must have the following metadata:

Metadata for "momentum"

Metadata	Names	Description
keys	"_"	the keys must have a single dimension named "_", with a single entry set to 0. The "momentum" quantity is always represented as a metatensor.torch.TensorMap with a single block.
samples	["system", "atom"]	the samples must be named ["system", "atom"], since "momentum" is always per-atom. "system" must range from 0 to the number of systems given as 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"	The "momentum" quantity must have a single component dimension named "xyz", with three entries set to 0, 1, and 2. The momentum is always a 3D vector, and the order of the components is x, y, z.
properties	"momentum"	The "momentum" quantity must have a single property dimension named "momentum", with a single entry set to 0.

"momentum" as model input

The following simulation engine can provide "momentum" as inputs to the models:

ASE

LAMMPS

i-PI

"momentum" as model output

The following simulation engine can use the "momentum" quantity as output:

LAMMPS

i-PI