Energy

Energy is associated with the "energy" key in the model outputs, and must have the following metadata:

Metadata for energy output

Metadata	Names	Description
keys	"_"	the energy keys must have a single dimension named "_", with a single entry set to 0. The energy is always a metatensor.torch.TensorMap with a single block.
samples	["system", "atom"] or ["system"]	if doing per_atom output, the sample names must be ["system", "atom"], otherwise the sample names must be ["system"]. "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		the energy must not have any components
properties	"energy"	the energy must have a single property dimension named "energy", with a single entry set to 0.

The following simulation engines can use the "energy" output:

LAMMPS

ASE

i-PI

Energy gradients

Most of the time when writing an atomistic model compatible with metatensor, gradients will be handled implicitly and computed by the simulation engine using a backward pass. Additionally, it is possible for the model to support explicit, forward mode gradients

The following gradients can be defined and requested with explicit_gradients:

• “positions” (\(r_j\)) gradients will contain the negative of the forces \(F_j\).

  \[\frac{\partial E}{\partial r_j} = -F_j\]

Metadata for positions energy’s gradients

Metadata	Names	Description
samples	["sample", "system", "atom"]	"sample" indicates which of the values samples we are taking the gradient of, and ("system", "atom") indicates which of the atom’s positions we are taking the gradients with respect to; i.e. \(j\) in the equation above.
components	"xyz"	there must be a single component named "xyz" with values 0, 1, 2; indicating the direction of the displacement of the atom in the gradient samples.

• “strain” (\(\epsilon\)) gradients will contain the stress \(\sigma\) acting on the system, multiplied by the volume \(V\) (sometimes also called the virial of this system)

  \[\frac{\partial E}{\partial \epsilon} = V \sigma\]

Metadata for strain energy’s gradients

Metadata	Names	Description
samples	"sample"	There is a single gradient sample dimension, "sample" indicating which of the values samples we are taking the gradient of.
components	["xyz_1", "xyz_2"]	Both "xyz_1" and "xyz_2" have values [0, 1, 2], and correspond to the two axes of the 3x3 strain matrix \(\epsilon\).

Energy ensemble

An ensemble of energies is associated with the "energy_ensemble" key in the model outputs. Such ensembles are sometimes used to perform uncertainty quantification, using multiple prediction to estimate an error on the mean prediction.

Energy ensembles must have the following metadata:

Metadata for energy ensemble output

Metadata	Names	Description
keys	same as Energy	same as Energy
samples	same as Energy	same as Energy
components	same as Energy	same as Energy
properties	"energy"	the energy ensemble must have a single property dimension named "energy", with entries ranging from 0 to the number of members of the ensemble minus one.

Currently, no simulation engines can use the "energy_ensemble" output.

Energy ensemble gradients

The gradient metadata for energy ensemble is the same as for the energy output (see Energy gradients).