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loss_metrics.py
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loss_metrics.py
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"""Content loss metrics for Sup3r"""
import numpy as np
import tensorflow as tf
from tensorflow.keras.losses import MeanAbsoluteError, MeanSquaredError
def gaussian_kernel(x1, x2, sigma=1.0):
"""Gaussian kernel for mmd content loss
Parameters
----------
x1 : tf.tensor
synthetic generator output
(n_obs, spatial_1, spatial_2, temporal, features)
x2 : tf.tensor
high resolution data
(n_obs, spatial_1, spatial_2, temporal, features)
sigma : float
Standard deviation for gaussian kernel
Returns
-------
tf.tensor
kernel output tensor
References
----------
Following MMD implementation in https://github.com/lmjohns3/theanets
"""
# The expand dims + subtraction compares every entry for the dimension
# prior to the expanded dimension to every other entry. So expand_dims with
# axis=1 will compare every observation along axis=0 to every other
# observation along axis=0.
result = tf.exp(-0.5 * tf.reduce_sum(
(tf.expand_dims(x1, axis=1) - x2)**2, axis=-1) / sigma**2)
return result
class ExpLoss(tf.keras.losses.Loss):
"""Loss class for squared exponential difference"""
def __call__(self, x1, x2):
"""Exponential difference loss function
Parameters
----------
x1 : tf.tensor
synthetic generator output
(n_observations, spatial_1, spatial_2, temporal, features)
x2 : tf.tensor
high resolution data
(n_observations, spatial_1, spatial_2, temporal, features)
Returns
-------
tf.tensor
0D tensor with loss value
"""
return tf.reduce_mean(1 - tf.exp(-(x1 - x2)**2))
class MseExpLoss(tf.keras.losses.Loss):
"""Loss class for mse + squared exponential difference"""
MSE_LOSS = MeanSquaredError()
def __call__(self, x1, x2):
"""Mse + Exponential difference loss function
Parameters
----------
x1 : tf.tensor
synthetic generator output
(n_observations, spatial_1, spatial_2, temporal, features)
x2 : tf.tensor
high resolution data
(n_observations, spatial_1, spatial_2, temporal, features)
Returns
-------
tf.tensor
0D tensor with loss value
"""
mse = self.MSE_LOSS(x1, x2)
exp = tf.reduce_mean(1 - tf.exp(-(x1 - x2)**2))
return mse + exp
class MmdLoss(tf.keras.losses.Loss):
"""Loss class for max mean discrepancy loss"""
def __call__(self, x1, x2, sigma=1.0):
"""Maximum mean discrepancy (MMD) based on Gaussian kernel function
for keras models
Parameters
----------
x1 : tf.tensor
synthetic generator output
(n_observations, spatial_1, spatial_2, temporal, features)
x2 : tf.tensor
high resolution data
(n_observations, spatial_1, spatial_2, temporal, features)
sigma : float
standard deviation for gaussian kernel
Returns
-------
tf.tensor
0D tensor with loss value
"""
mmd = tf.reduce_mean(gaussian_kernel(x1, x1, sigma))
mmd += tf.reduce_mean(gaussian_kernel(x2, x2, sigma))
mmd -= tf.reduce_mean(2 * gaussian_kernel(x1, x2, sigma))
return mmd
class MmdMseLoss(tf.keras.losses.Loss):
"""Loss class for MMD + MSE"""
MMD_LOSS = MmdLoss()
MSE_LOSS = MeanSquaredError()
def __call__(self, x1, x2, sigma=1.0):
"""Maximum mean discrepancy (MMD) based on Gaussian kernel function
for keras models plus the typical MSE loss.
Parameters
----------
x1 : tf.tensor
synthetic generator output
(n_observations, spatial_1, spatial_2, temporal, features)
x2 : tf.tensor
high resolution data
(n_observations, spatial_1, spatial_2, temporal, features)
sigma : float
standard deviation for gaussian kernel
Returns
-------
tf.tensor
0D tensor with loss value
"""
mmd = self.MMD_LOSS(x1, x2, sigma=sigma)
mse = self.MSE_LOSS(x1, x2)
return (mmd + mse) / 2
class CoarseMseLoss(tf.keras.losses.Loss):
"""Loss class for coarse mse on spatial average of 5D tensor"""
MSE_LOSS = MeanSquaredError()
def __call__(self, x1, x2):
"""Exponential difference loss function
Parameters
----------
x1 : tf.tensor
synthetic generator output
(n_observations, spatial_1, spatial_2, temporal, features)
x2 : tf.tensor
high resolution data
(n_observations, spatial_1, spatial_2, temporal, features)
Returns
-------
tf.tensor
0D tensor with loss value
"""
x1_coarse = tf.reduce_mean(x1, axis=(1, 2))
x2_coarse = tf.reduce_mean(x2, axis=(1, 2))
return self.MSE_LOSS(x1_coarse, x2_coarse)
class SpatialExtremesOnlyLoss(tf.keras.losses.Loss):
"""Loss class that encourages accuracy of the min/max values in the
spatial domain. This does not include an additional MAE term"""
MAE_LOSS = MeanAbsoluteError()
def __call__(self, x1, x2):
"""Custom content loss that encourages temporal min/max accuracy
Parameters
----------
x1 : tf.tensor
synthetic generator output
(n_observations, spatial_1, spatial_2, features)
x2 : tf.tensor
high resolution data
(n_observations, spatial_1, spatial_2, features)
Returns
-------
tf.tensor
0D tensor with loss value
"""
x1_min = tf.reduce_min(x1, axis=(1, 2))
x2_min = tf.reduce_min(x2, axis=(1, 2))
x1_max = tf.reduce_max(x1, axis=(1, 2))
x2_max = tf.reduce_max(x2, axis=(1, 2))
mae_min = self.MAE_LOSS(x1_min, x2_min)
mae_max = self.MAE_LOSS(x1_max, x2_max)
return (mae_min + mae_max) / 2
class SpatialExtremesLoss(tf.keras.losses.Loss):
"""Loss class that encourages accuracy of the min/max values in the
spatial domain"""
MAE_LOSS = MeanAbsoluteError()
EX_LOSS = SpatialExtremesOnlyLoss()
def __init__(self, weight=1.0):
"""Initialize the loss with given weight
Parameters
----------
weight : float
Weight for min/max loss terms. Setting this to zero turns
loss into MAE.
"""
super().__init__()
self._weight = weight
def __call__(self, x1, x2):
"""Custom content loss that encourages temporal min/max accuracy
Parameters
----------
x1 : tf.tensor
synthetic generator output
(n_observations, spatial_1, spatial_2, features)
x2 : tf.tensor
high resolution data
(n_observations, spatial_1, spatial_2, features)
Returns
-------
tf.tensor
0D tensor with loss value
"""
mae = self.MAE_LOSS(x1, x2)
ex_mae = self.EX_LOSS(x1, x2)
return (mae + 2 * self._weight * ex_mae) / 3
class TemporalExtremesOnlyLoss(tf.keras.losses.Loss):
"""Loss class that encourages accuracy of the min/max values in the
timeseries. This does not include an additional mae term"""
MAE_LOSS = MeanAbsoluteError()
def __call__(self, x1, x2):
"""Custom content loss that encourages temporal min/max accuracy
Parameters
----------
x1 : tf.tensor
synthetic generator output
(n_observations, spatial_1, spatial_2, temporal, features)
x2 : tf.tensor
high resolution data
(n_observations, spatial_1, spatial_2, temporal, features)
Returns
-------
tf.tensor
0D tensor with loss value
"""
x1_min = tf.reduce_min(x1, axis=3)
x2_min = tf.reduce_min(x2, axis=3)
x1_max = tf.reduce_max(x1, axis=3)
x2_max = tf.reduce_max(x2, axis=3)
mae_min = self.MAE_LOSS(x1_min, x2_min)
mae_max = self.MAE_LOSS(x1_max, x2_max)
return (mae_min + mae_max) / 2
class TemporalExtremesLoss(tf.keras.losses.Loss):
"""Loss class that encourages accuracy of the min/max values in the
timeseries"""
MAE_LOSS = MeanAbsoluteError()
EX_LOSS = TemporalExtremesOnlyLoss()
def __init__(self, weight=1.0):
"""Initialize the loss with given weight
Parameters
----------
weight : float
Weight for min/max loss terms. Setting this to zero turns
loss into MAE.
"""
super().__init__()
self._weight = weight
def __call__(self, x1, x2):
"""Custom content loss that encourages temporal min/max accuracy
Parameters
----------
x1 : tf.tensor
synthetic generator output
(n_observations, spatial_1, spatial_2, temporal, features)
x2 : tf.tensor
high resolution data
(n_observations, spatial_1, spatial_2, temporal, features)
Returns
-------
tf.tensor
0D tensor with loss value
"""
mae = self.MAE_LOSS(x1, x2)
ex_mae = self.EX_LOSS(x1, x2)
return (mae + 2 * self._weight * ex_mae) / 3
class SpatiotemporalExtremesLoss(tf.keras.losses.Loss):
"""Loss class that encourages accuracy of the min/max values across both
space and time"""
MAE_LOSS = MeanAbsoluteError()
S_EX_LOSS = SpatialExtremesOnlyLoss()
T_EX_LOSS = TemporalExtremesOnlyLoss()
def __init__(self, spatial_weight=1.0, temporal_weight=1.0):
"""Initialize the loss with given weight
Parameters
----------
spatial_weight : float
Weight for spatial min/max loss terms.
temporal_weight : float
Weight for temporal min/max loss terms.
"""
super().__init__()
self.s_weight = spatial_weight
self.t_weight = temporal_weight
def __call__(self, x1, x2):
"""Custom content loss that encourages spatiotemporal min/max accuracy.
Parameters
----------
x1 : tf.tensor
synthetic generator output
(n_observations, spatial_1, spatial_2, temporal, features)
x2 : tf.tensor
high resolution data
(n_observations, spatial_1, spatial_2, temporal, features)
Returns
-------
tf.tensor
0D tensor with loss value
"""
mae = self.MAE_LOSS(x1, x2)
s_ex_mae = self.S_EX_LOSS(x1, x2)
t_ex_mae = self.T_EX_LOSS(x1, x2)
return (mae + 2 * self.s_weight * s_ex_mae
+ 2 * self.t_weight * t_ex_mae) / 5
class SpatialFftOnlyLoss(tf.keras.losses.Loss):
"""Loss class that encourages accuracy of the spatial frequency spectrum"""
MAE_LOSS = MeanAbsoluteError()
@staticmethod
def _freq_weights(x):
"""Get product of squared frequencies to weight frequency amplitudes"""
k0 = np.array([k**2 for k in range(x.shape[1])])
k1 = np.array([k**2 for k in range(x.shape[2])])
freqs = np.multiply.outer(k0, k1)
freqs = tf.convert_to_tensor(freqs[np.newaxis, ..., np.newaxis])
return tf.cast(freqs, x.dtype)
def _fft(self, x):
"""Apply needed transpositions and fft operation."""
x_hat = tf.transpose(x, perm=[3, 0, 1, 2])
x_hat = tf.signal.fft2d(tf.cast(x_hat, tf.complex64))
x_hat = tf.transpose(x_hat, perm=[1, 2, 3, 0])
x_hat = tf.cast(tf.abs(x_hat), x.dtype)
x_hat = tf.math.multiply(self._freq_weights(x), x_hat)
return tf.math.log(1 + x_hat)
def __call__(self, x1, x2):
"""Custom content loss that encourages frequency domain accuracy
Parameters
----------
x1 : tf.tensor
synthetic generator output
(n_observations, spatial_1, spatial_2, features)
x2 : tf.tensor
high resolution data
(n_observations, spatial_1, spatial_2, features)
Returns
-------
tf.tensor
0D tensor with loss value
"""
x1_hat = self._fft(x1)
x2_hat = self._fft(x2)
return self.MAE_LOSS(x1_hat, x2_hat)
class SpatiotemporalFftOnlyLoss(tf.keras.losses.Loss):
"""Loss class that encourages accuracy of the spatiotemporal frequency
spectrum"""
MAE_LOSS = MeanAbsoluteError()
@staticmethod
def _freq_weights(x):
"""Get product of squared frequencies to weight frequency amplitudes"""
k0 = np.array([k**2 for k in range(x.shape[1])])
k1 = np.array([k**2 for k in range(x.shape[2])])
f = np.array([f**2 for f in range(x.shape[3])])
freqs = np.multiply.outer(k0, k1)
freqs = np.multiply.outer(freqs, f)
freqs = tf.convert_to_tensor(freqs[np.newaxis, ..., np.newaxis])
return tf.cast(freqs, x.dtype)
def _fft(self, x):
"""Apply needed transpositions and fft operation."""
x_hat = tf.transpose(x, perm=[4, 0, 1, 2, 3])
x_hat = tf.signal.fft3d(tf.cast(x_hat, tf.complex64))
x_hat = tf.transpose(x_hat, perm=[1, 2, 3, 4, 0])
x_hat = tf.cast(tf.abs(x_hat), x.dtype)
x_hat = tf.math.multiply(self._freq_weights(x), x_hat)
return tf.math.log(1 + x_hat)
def __call__(self, x1, x2):
"""Custom content loss that encourages frequency domain accuracy
Parameters
----------
x1 : tf.tensor
synthetic generator output
(n_observations, spatial_1, spatial_2, temporal, features)
x2 : tf.tensor
high resolution data
(n_observations, spatial_1, spatial_2, temporal, features)
Returns
-------
tf.tensor
0D tensor with loss value
"""
x1_hat = self._fft(x1)
x2_hat = self._fft(x2)
return self.MAE_LOSS(x1_hat, x2_hat)
class StExtremesFftLoss(tf.keras.losses.Loss):
"""Loss class that encourages accuracy of the min/max values across both
space and time as well as frequency domain accuracy."""
def __init__(self, spatial_weight=1.0, temporal_weight=1.0,
fft_weight=1.0):
"""Initialize the loss with given weight
Parameters
----------
spatial_weight : float
Weight for spatial min/max loss terms.
temporal_weight : float
Weight for temporal min/max loss terms.
fft_weight : float
Weight for the fft loss term.
"""
super().__init__()
self.st_ex_loss = SpatiotemporalExtremesLoss(spatial_weight,
temporal_weight)
self.fft_loss = SpatiotemporalFftOnlyLoss()
self.fft_weight = fft_weight
def __call__(self, x1, x2):
"""Custom content loss that encourages spatiotemporal min/max accuracy
and fft accuracy.
Parameters
----------
x1 : tf.tensor
synthetic generator output
(n_observations, spatial_1, spatial_2, temporal, features)
x2 : tf.tensor
high resolution data
(n_observations, spatial_1, spatial_2, temporal, features)
Returns
-------
tf.tensor
0D tensor with loss value
"""
return (5 * self.st_ex_loss(x1, x2)
+ self.fft_weight * self.fft_loss(x1, x2)) / 6
class LowResLoss(tf.keras.losses.Loss):
"""Content loss that is calculated by coarsening the synthetic and true
high-resolution data pairs and then performing the pointwise content loss
on the low-resolution fields"""
def __init__(self, s_enhance=1, t_enhance=1, t_method='average',
tf_loss='MeanSquaredError'):
"""Initialize the loss with given weight
Parameters
----------
s_enhance : int
factor by which to coarsen spatial dimensions. 1 will keep the
spatial axes as high-res
t_enhance : int
factor by which to coarsen temporal dimension. 1 will keep the
temporal axes as high-res
t_method : str
Accepted options: [subsample, average]
Subsample will take every t_enhance-th time step, average will
average over t_enhance time steps
tf_loss : str
The tensorflow loss function to operate on the low-res fields. Must
be the name of a loss class that can be retrieved from
``tf.keras.losses`` e.g., "MeanSquaredError" or "MeanAbsoluteError"
"""
super().__init__()
self._s_enhance = s_enhance
self._t_enhance = t_enhance
self._t_method = str(t_method).casefold()
self._tf_loss = getattr(tf.keras.losses, tf_loss)()
def _s_coarsen_4d_tensor(self, tensor):
"""Perform spatial coarsening on a 4D tensor of shape
(n_obs, spatial_1, spatial_2, features)"""
shape = tensor.shape
tensor = tf.reshape(tensor,
(shape[0],
shape[1] // self._s_enhance, self._s_enhance,
shape[2] // self._s_enhance, self._s_enhance,
shape[3]))
tensor = tf.math.reduce_sum(tensor, axis=(2, 4)) / self._s_enhance**2
return tensor
def _s_coarsen_5d_tensor(self, tensor):
"""Perform spatial coarsening on a 5D tensor of shape
(n_obs, spatial_1, spatial_2, time, features)"""
shape = tensor.shape
tensor = tf.reshape(tensor,
(shape[0],
shape[1] // self._s_enhance, self._s_enhance,
shape[2] // self._s_enhance, self._s_enhance,
shape[3], shape[4]))
tensor = tf.math.reduce_sum(tensor, axis=(2, 4)) / self._s_enhance**2
return tensor
def _t_coarsen_sample(self, tensor):
"""Perform temporal subsampling on a 5D tensor of shape
(n_obs, spatial_1, spatial_2, time, features)"""
assert len(tensor.shape) == 5
tensor = tensor[:, :, :, ::self._t_enhance, :]
return tensor
def _t_coarsen_avg(self, tensor):
"""Perform temporal coarsening on a 5D tensor of shape
(n_obs, spatial_1, spatial_2, time, features)"""
shape = tensor.shape
assert len(shape) == 5
tensor = tf.reshape(tensor, (shape[0], shape[1], shape[2], -1,
self._t_enhance, shape[4]))
tensor = tf.math.reduce_sum(tensor, axis=4) / self._t_enhance
return tensor
def __call__(self, x1, x2):
"""Custom content loss calculated on re-coarsened low-res fields
Parameters
----------
x1 : tf.tensor
Synthetic high-res generator output, shape is either of these:
(n_obs, spatial_1, spatial_2, features)
(n_obs, spatial_1, spatial_2, temporal, features)
x2 : tf.tensor
True high resolution data, shape is either of these:
(n_obs, spatial_1, spatial_2, features)
(n_obs, spatial_1, spatial_2, temporal, features)
Returns
-------
tf.tensor
0D tensor loss value
"""
assert x1.shape == x2.shape
s_only = len(x1.shape) == 4
if self._s_enhance > 1 and s_only:
x1 = self._s_coarsen_4d_tensor(x1)
x2 = self._s_coarsen_4d_tensor(x2)
elif self._s_enhance > 1 and not s_only:
x1 = self._s_coarsen_5d_tensor(x1)
x2 = self._s_coarsen_5d_tensor(x2)
if self._t_enhance > 1 and self._t_method == 'average':
x1 = self._t_coarsen_avg(x1)
x2 = self._t_coarsen_avg(x2)
if self._t_enhance > 1 and self._t_method == 'subsample':
x1 = self._t_coarsen_sample(x1)
x2 = self._t_coarsen_sample(x2)
return self._tf_loss(x1, x2)