Loss function

Contents

Loss function#

The following shows the loss function to be optimized during the training.

Definition#

\[L \equiv w_\mathrm{e} L_\mathrm{e} + w_\mathrm{f} L_\mathrm{f} + w_\mathrm{s} L_\mathrm{s}\]

  • \(L_\mathrm{e}\): contribution from energy

    • energy_per_atom = true:

      \[L_\mathrm{e} \equiv \sum_{k=1}^{N_\mathrm{conf}} (\hat{E}_k - \hat{E}_k^\mathrm{ref})^2\]

      where

      \[\hat{E}_k \equiv \frac{E_k}{N_{\mathrm{atom},k}}\]

  • \(L_\mathrm{f}\): Contribution from forces

    • forces_per_atom = true:

      \[L_\mathrm{f} \equiv \sum_{k=1}^{N_\mathrm{conf}} \frac{1}{N_{\mathrm{atom},k}} \sum_{i=1}^{N_{\mathrm{atom},k}} \sum_{\alpha=1}^{3} (F_{k,i\alpha} - F_{k,i\alpha}^\mathrm{ref})^2\]

  • \(L_\mathrm{s}\): Contribution from stress

    • stress_times_volume = true:

      \[L_\mathrm{s} \equiv \sum_{k=1}^{N_\mathrm{conf}} V_k^2 \sum_{\alpha=1}^{3} \sum_{\beta=1}^{3} (\sigma_{k,\alpha\beta} - \sigma_{k,\alpha\beta}^\mathrm{ref})^2\]

      energy_per_atom is also respected.

Default#

motep.toml

[loss]
energy_weight = 1.0
forces_weight = 0.01
stress_weight = 0.001
energy_per_atom = true
forces_per_atom = true
stress_times_volume = true
energy_per_conf = true
forces_per_conf = true
stress_per_conf = true
Contents