# MIT License
#
# Copyright (c) 2020-2023, Alex M. Maldonado
#
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# of this software and associated documentation files (the "Software"), to deal
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# SOFTWARE.
import numpy as np
from .logger import GDMLLogger
log = GDMLLogger(__name__)
[docs]def mae(errors):
r"""Mean absolute error (MAE).
.. math::
MAE = \frac{1}{n} \sum_{i=1}^n \mid \hat{y}_{i} - y_{i} \mid,
where :math:`y_{i}` is the true value, :math:`\hat{y}_{i}` is the
predicted value, :math:`\mid \cdots \mid` is the absolute value, and
:math:`n` is the number of data points.
Parameters
----------
errors : :obj:`numpy.ndarray`
Array of :math:`\hat{y} - y` values. This will be flattened beforehand.
Returns
-------
:obj:`float`
Mean absolute error.
See Also
--------
mse, rmse, sse
"""
return np.mean(np.abs(errors.flatten()))
[docs]def mse(errors):
r"""Mean squared error (MSE).
.. math::
MSE = \frac{1}{n} \sum_{i=1}^n \left( \hat{y}_{i} - y_{i} \right)^2,
where :math:`y_{i}` is the true value, :math:`\hat{y}_{i}` is the
predicted value, and :math:`n` is the number of data points.
Parameters
----------
errors : :obj:`numpy.ndarray`
Array of :math:`\hat{y} - y` values. This will be flattened beforehand.
Returns
-------
:obj:`float`
Mean squared error.
See Also
--------
mae, rmse, sse
"""
return np.mean(errors.flatten() ** 2)
[docs]def rmse(errors):
r"""Root-mean-squared error.
.. math::
RMSE = \sqrt{ \frac{\sum_{i=1}^n \left( \hat{y}_{i} - y_{i} \right)^2}{n} },
where :math:`y_{i}` is the true value, :math:`\hat{y}_{i}` is the
predicted value, and :math:`n` is the number of data points.
Parameters
----------
errors : :obj:`numpy.ndarray`
Array of :math:`\hat{y} - y` values. This will be flattened beforehand.
Returns
-------
:obj:`float`
Root-mean-squared error.
See Also
--------
mae, mse, sse
"""
return np.sqrt(mse(errors))
[docs]def sse(errors):
r"""Sum of squared errors.
.. math::
SSE = \sum_{i=1}^n \left( \hat{y}_{i} - y_{i} \right)^2,
where :math:`y_{i}` is the true value, :math:`\hat{y}_{i}` is the
predicted value, and :math:`n` is the number of data points.
Parameters
----------
errors : :obj:`numpy.ndarray`
Array of :math:`\hat{y} - y` values. This will be flattened beforehand.
Returns
-------
:obj:`float`
Sum of squared errors.
See Also
--------
mae, mse, rmse
"""
return np.dot(errors.flatten(), errors.flatten())
[docs]def loss_f_mse(results):
r"""Force MSE.
Parameters
----------
results : :obj:`dict`
Results which contains at least force errors under the ``'force'`` key.
Returns
-------
:obj:`float`
Loss.
See Also
--------
loss_f_rmse, loss_f_e_weighted_mse
"""
return mse(results["force"])
[docs]def loss_f_rmse(results):
r"""Force RMSE.
Parameters
----------
results : :obj:`dict`
Results which contains at least force errors under the ``'force'`` key.
Returns
-------
:obj:`float`
Loss.
"""
return rmse(results["force"])
[docs]def loss_f_e_weighted_mse(results, rho, n_atoms):
r"""Computes a combined energy and force loss function.
.. math::
l = \frac{\rho}{Q} \left\Vert E - \hat{E} \right\Vert^2
+ \frac{1}{n_{atoms} Q} \sum_{i=0}^{n_{atoms}}
\left\Vert \bf{F}_i - \widehat{\bf{F}}_i \right\Vert^2,
where :math:`\rho` is a trade-off between energy and force errors,
:math:`Q` is the number of validation structures, :math:`\Vert \ldots \Vert`
is the norm, and :math:`\widehat{\;}` is the model prediction of the
property.
Parameters
----------
results : :obj:`dict`
Results which contains at least force and energy errors under the
``'force'`` and ``'energy'`` keys, respectively.
rho : :obj:`float`
Energy and force trade-off, :math:`\rho`. A recommended value would be
in the range of ``0.01`` to ``0.1``. Larger values place more
importance on energy accuracy.
n_atoms : :obj:`int`
Number of atoms.
Returns
-------
:obj:`float`
Loss.
"""
F_mse = mse(results["force"])
E_mse = mse(results["energy"])
return rho * E_mse + (1 / n_atoms) * F_mse