Non-conservative forces

Non-conservative forces are forces that are not calculated as the negative gradient of a potential energy function. These are generally faster to compute than forces derived from the potential energy by backpropagation. However, these predictions must be used with care, see https://arxiv.org/abs/2412.11569.

In metatomic models, they are associated with the "non_conservative_forces" or "non_conservative_forces/<variant>" key (see Output variants) in the model outputs, and must adhere to the following metadata schema:

Metadata for non-conservative forces

Metadata	Names	Description
keys	"_"	the keys must have a single dimension named "_", with a single entry set to 0. Non-conservative forces are always a metatensor.torch.TensorMap with a single block.
samples	["system", "atom"]	the samples must be named ["system", "atom"], since non-conservative forces 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"	non-conservative forces must have a single component dimension named "xyz", with three entries set to 0, 1, and 2. The non-conservative forces are always 3D vectors, and the order of the components is x, y, z.
properties	"non_conservative_forces"	non-conservative forces must have a single property dimension named "non_conservative_forces", with a single entry set to 0.

The following simulation engines can use the "non_conservative_forces" output, using a non_conservative flag:

ASE

i-PI

LAMMPS

Note

If you are adding support for non_conservative_forces in a molecular dynamics engine, metatomic models might predict a non zero total force. You should consider removing this total force to prevent drift in your simulations.

Non-conservative stress

Similar to the forces, the “non-conservative stress” is a stress tensor that is not calculated using derivatives of the potential energy. As with forces, they are typically faster to compute but need to be used with care, see https://arxiv.org/abs/2412.11569.

In metatomic models, they are associated with the "non_conservative_stress" or "non_conservative_stress/<variant>" key (see Output variants) in the model outputs, and must adhere to the following metadata schema:

Metadata for non-conservative stress output

Metadata	Names	Description
keys	"_"	the keys must have a single dimension named "_", with a single entry set to 0. Non-conservative forces are always a metatensor.torch.TensorMap with a single block.
samples	"system"	the samples should contain a single sample named "system" The values must range from 0 to the number of systems given as input to the model.
components	["xyz_1"], ["xyz_2"]	the non-conservative stress must have two components labels with "xyz_1" and "xyz_2" as their respective names, both with three entries set to 0, 1, and 2. The order of the components along both directions is x, y, z.
properties	"non_conservative_stress"	the non-conservative stress must have a single property dimension named "non_conservative_stress", with a single entry set to 0.

The following simulation engines can use the "non_conservative_stress" output, using a non_conservative flag:

ASE

i-PI

LAMMPS