Potential Model

Atomic dress

The absolute value of total energy from ab-initio calculations can often be very large. To avoid numerical problems, it is common practice to assign a constant atomic energy (dress) to each type of atom, such that the average energy is shifted to zero. Such an atomic dress can be generated with pinn.utils.get_atomic_dress

Loss function

The loss function in potential model is defined as following:

\[ L = w_e \cdot \mathrm{MSE}(e) + w_f \cdot \mathrm{MSE}(f) + w_s \cdot \mathrm{MSE} (s) + \mathrm{regularization} \]

Loss terms are mean squared errors of:

\(e\): energies
\(f\): forces components
\(s\): stress tensor components

It is assumed that the energy, force and stress labels are labelled as "e_data", "f_data", "s_data" in the training set respectively, if they are to be used in the loss function.

Parameters

Below is a list of additional parameters of the potential model and their descriptions.

Parameter	Default	Description
`e_dress`	`{}`	Atomic Dress
`e_scale`	`1`	The energy scaling during training, this variable defines the energy unit during training
`e_unit`	`1`	Unit of the input energies, this variable will be used in the ASE calculator
`max_energy`	`False`	When set to a number, exclude energies above this value in loss function
`use_e_per_atom`	`False`	Use the per-atom energy in place of total energy in loss function
`log_e_per_atom`	`True`	Log the per-atom energy error, automatically enabled with `use_e_per_atoms=True`
`use_e_weight`	`False`	Scale the energy loss according to the `'e_weight'` Tensor in the dataset
`use_force`	`False`	Include force in loss function
`max_force_comp`	`False`	if set to float, omit forces components larger than it
`no_force_comp`	`False`	if set to int, use as maximum number of force component per weight update
`use_f_weights`	`False`	Scale the energy loss according to the `'f_weights'` Tensor in the dataset
`use_stress`	`False`	Include stress in loss function
`use_l2`	`False`	Include L2 regularization in loss function
`e_loss_multiplier`	`1`	Weight of energy loss
`f_loss_multiplier`	`1`	Weight of force loss
`s_loss_multiplier`	`1`	Weight of stress loss
`l2_loss_multiplier`	`1`	Weight of l2 loss

ASE calculator

A calculator can be created from a model as simple as:

from pinn.get_calc
calc = get_calc('/path/to/model/')
calc.calculate(atoms)
calc.get_forces()

Units

Following the convention of ASE, the output unit is eV for energy, eV/Å for forces and eV/Å³ for stress tensor. Since PiNN does not know about the unit in the dataset, a to_eV parameter is given to convert from the dataset unit to eV (this optional is not necessary if e_unit is set in the parameters).

Available results

energy: total energy
forces: forces
energies: atomic contribution to the energy
stress: stress tensor