This keyword can be used to bias the loss function to put more emphasis on obtaining accurate predictions for smaller forces. The syntax is:

force_delta <delta>

where <delta> sets the parameter \(\delta\), which must satisfy \(\delta \geq 0\) eV/A and defaults to \(\delta = 0\) eV/A (i.e., no bias).

When \(\delta = 0\) eV/A, the loss term associated with the forces is proportional to the RMSE of the forces:

\[\sqrt{\frac{1}{3N}\sum_{i=1}^{N}\left(\boldsymbol{F}_i^\mathrm{NEP} - \boldsymbol{F}_i^\mathrm{tar}\right)^2}\]

When \(\delta > 0\) eV/Å, this expression is modified to read:

\[\sqrt{\frac{1}{3N}\sum_{i=1}^{N}\left(\boldsymbol{F}_i^\mathrm{NEP} - \boldsymbol{F}_i^\mathrm{tar}\right)^2 \frac{1}{1+\|\boldsymbol{F}_i^\mathrm{tar}\| / \delta} }\]

In this case, a smaller \(\delta\) implies a larger weight on smaller forces.