def _mg_solve_forward(divergence, domain, pressure_guess, solvers):
fluid_mask = domain.accessible_tensor(extend=1)
active_mask = domain.active_tensor(extend=1)
if active_mask is not None or fluid_mask is not None:
if not np.all([s.supports_continuous_masks for s in solvers[:-1]]):
logging.warning(
"MultiscaleSolver solver: There are boundary conditions inside the domain but "
"not all intermediate solvers support continuous masks")
div_lvls = [divergence]
act_lvls = [active_mask]
fld_lvls = [fluid_mask]
for grid_i in range(len(solvers) - 1):
div_lvls.insert(0, math.downsample2x(div_lvls[0]))
act_lvls.insert(
0,
math.downsample2x(act_lvls[0])
if act_lvls[0] is not None else None)
fld_lvls.insert(
0,
math.downsample2x(fld_lvls[0])
if fld_lvls[0] is not None else None)
if pressure_guess is not None:
pressure_guess = math.downsample2x(pressure_guess)
iter_list = []
for i, div in enumerate(div_lvls):
pressure_guess, iteration = solvers[i].solve(
div, FluidDomain(act_lvls[i], fld_lvls[i], boundaries),
pressure_guess)
iter_list.append(iteration)
if pressure_guess.shape[1] < divergence.shape[1]:
pressure_guess = math.upsample2x(
pressure_guess) * 2**math.spatial_rank(divergence)
return pressure_guess, iter_list
def upsample_apply(params, inputs, **kwargs):
x = math.wrap(
inputs, math.batch('batch'),
*[math.spatial(f'{i}') for i in range(len(inputs.shape) - 2)],
math.channel('vector'))
x = math.upsample2x(x)
return x.native(x.shape)
def test_upsample2x(self):
meshgrid = math.meshgrid(x=(0, 1, 2, 3), y=(0, -1, -2))
double_size = math.upsample2x(meshgrid, extrapolation.BOUNDARY)
same_size = math.downsample2x(double_size)
math.print(meshgrid, 'Normal size')
math.print(double_size, 'Double size')
math.print(same_size, 'Same size')
math.assert_close(meshgrid.x[1:-1].y[1:-1], same_size.x[1:-1].y[1:-1])
def upsample2x(grid: GridType) -> GridType:
if isinstance(grid, CenteredGrid):
values = math.upsample2x(grid.values, grid.extrapolation)
return CenteredGrid(values, grid.bounds, grid.extrapolation)
elif isinstance(grid, StaggeredGrid):
raise NotImplementedError()
else:
raise ValueError(type(grid))
def upsample2x(grid: GridType) -> GridType:
"""
Increases the number of sample points by a factor of 2 in each spatial dimension.
The new values are determined via linear interpolation.
See Also:
`downsample2x()`.
Args:
grid: `CenteredGrid` or `StaggeredGrid`.
Returns:
`Grid` of same type as `grid`.
"""
if isinstance(grid, CenteredGrid):
values = math.upsample2x(grid.values, grid.extrapolation)
return CenteredGrid(values,
bounds=grid.bounds,
extrapolation=grid.extrapolation)
elif isinstance(grid, StaggeredGrid):
raise NotImplementedError()
else:
raise ValueError(type(grid))
def pressure_unet(divergence, scope="pressure_unet"):
with tf.variable_scope(scope):
x = divergence
print(x.shape)
# DownConv Level 1
c1 = tf.layers.conv2d(x, 4, 5, strides=1, activation=tf.nn.relu, padding="same", name="conv1", trainable=True,
reuse=tf.AUTO_REUSE)
c2 = tf.layers.conv2d(c1, 4, 5, strides=1, activation=tf.nn.relu, padding="same", name="conv2", trainable=True,
reuse=tf.AUTO_REUSE)
c3 = tf.layers.conv2d(c2, 4, 5, strides=2, activation=tf.nn.relu, padding="same", name="conv3", trainable=True,
reuse=tf.AUTO_REUSE)
print(c3.shape)
# DownConv Level 2
c4 = tf.layers.conv2d(c3, 8, 5, strides=1, activation=tf.nn.relu, padding="same", name="conv4", trainable=True,
reuse=tf.AUTO_REUSE)
c5 = tf.layers.conv2d(c4, 8, 5, strides=1, activation=tf.nn.relu, padding="same", name="conv5", trainable=True,
reuse=tf.AUTO_REUSE)
c6 = tf.layers.conv2d(c5, 8, 5, strides=2, activation=tf.nn.relu, padding="same", name="conv6", trainable=True,
reuse=tf.AUTO_REUSE)
print(c6.shape)
# DownConv Level 3
c7 = tf.layers.conv2d(c6, 16, 5, strides=1, activation=tf.nn.relu, padding="same", name="conv7", trainable=True,
reuse=tf.AUTO_REUSE)
c8 = tf.layers.conv2d(c7, 16, 5, strides=1, activation=tf.nn.relu, padding="same", name="conv8", trainable=True,
reuse=tf.AUTO_REUSE)
c9 = tf.layers.conv2d(c8, 16, 5, strides=2, activation=tf.nn.relu, padding="same", name="conv9", trainable=True,
reuse=tf.AUTO_REUSE)
print(c9.shape)
# Lowest Convolutions
c10 = tf.layers.conv2d(c9, 32, 5, strides=1, activation=tf.nn.relu, padding="same", name="conv10", trainable=True,
reuse=tf.AUTO_REUSE)
c11 = tf.layers.conv2d(c10, 32, 5, strides=1, activation=tf.nn.relu, padding="same", name="conv11", trainable=True,
reuse=tf.AUTO_REUSE)
c12 = tf.layers.conv2d(c11, 32, 5, strides=1, activation=tf.nn.relu, padding="same", name="conv12", trainable=True,
reuse=tf.AUTO_REUSE)
print(c12.shape)
# UpConv Level 3
u1 = upsample2x(c12)
uc1 = tf.layers.conv2d(tf.concat([u1, c8], 3), 16, 5, strides=1, activation=tf.nn.relu, padding="same",
name="upconv1", trainable=True, reuse=tf.AUTO_REUSE)
uc2 = tf.layers.conv2d(uc1, 16, 5, strides=1, activation=tf.nn.relu, padding="same", name="upconv2",
trainable=True, reuse=tf.AUTO_REUSE)
uc3 = tf.layers.conv2d(uc2, 16, 5, strides=1, activation=tf.nn.relu, padding="same", name="upconv3",
trainable=True, reuse=tf.AUTO_REUSE)
print(uc3.shape)
# UpConv Level 2
u2 = upsample2x(uc3)
uc4 = tf.layers.conv2d(tf.concat([u2, c5], 3), 8, 5, strides=1, activation=tf.nn.relu, padding="same",
name="upconv4", trainable=True, reuse=tf.AUTO_REUSE)
uc5 = tf.layers.conv2d(uc4, 8, 5, strides=1, activation=tf.nn.relu, padding="same", name="upconv5",
trainable=True, reuse=tf.AUTO_REUSE)
uc6 = tf.layers.conv2d(uc5, 8, 5, strides=1, activation=tf.nn.relu, padding="same", name="upconv6",
trainable=True, reuse=tf.AUTO_REUSE)
print(uc6.shape)
# UpConv Level 1
u3 = upsample2x(uc6)
uc7 = tf.layers.conv2d(tf.concat([u3, c2], 3), 4, 5, strides=1, activation=tf.nn.relu, padding="same",
name="upconv7", trainable=True, reuse=tf.AUTO_REUSE)
uc8 = tf.layers.conv2d(uc7, 4, 5, strides=1, activation=tf.nn.relu, padding="same", name="upconv8",
trainable=True, reuse=tf.AUTO_REUSE)
uc9 = tf.layers.conv2d(uc8, 4, 5, strides=1, activation=tf.nn.relu, padding="same", name="upconv9",
trainable=True, reuse=tf.AUTO_REUSE)
print(uc9.shape)
# final Convolution
out = tf.layers.conv2d(uc9, 1, 5, strides=1, activation=None, padding="same", name="out_conv", trainable=True,
reuse=tf.AUTO_REUSE)
return out
def pressure_unet(divergence, geometry_mask=None, scope="pressure_unet"):
""" Network structure (Based on U-Net) """
with tf.variable_scope(scope):
x = divergence
if geometry_mask is not None:
g_mask = tf.broadcast_to(geometry_mask, tf.shape(x)) # broadcast same mask across batch
x = tf.concat([x, g_mask], axis=3) # concatenate mask to divergence
print(x.shape)
# DownConv Level 1
c1 = tf.layers.conv2d(x, 4, 5, strides=1, activation=tf.nn.relu, padding="same", name="conv1", trainable=True,
reuse=tf.AUTO_REUSE)
c2 = tf.layers.conv2d(c1, 4, 5, strides=1, activation=tf.nn.relu, padding="same", name="conv2", trainable=True,
reuse=tf.AUTO_REUSE)
c3 = tf.layers.conv2d(c2, 4, 5, strides=2, activation=tf.nn.relu, padding="same", name="conv3", trainable=True,
reuse=tf.AUTO_REUSE)
print(c3.shape)
# DownConv Level 2
c4 = tf.layers.conv2d(c3, 8, 5, strides=1, activation=tf.nn.relu, padding="same", name="conv4", trainable=True,
reuse=tf.AUTO_REUSE)
c5 = tf.layers.conv2d(c4, 8, 5, strides=1, activation=tf.nn.relu, padding="same", name="conv5", trainable=True,
reuse=tf.AUTO_REUSE)
c6 = tf.layers.conv2d(c5, 8, 5, strides=2, activation=tf.nn.relu, padding="same", name="conv6", trainable=True,
reuse=tf.AUTO_REUSE)
print(c6.shape)
# DownConv Level 3
c7 = tf.layers.conv2d(c6, 16, 5, strides=1, activation=tf.nn.relu, padding="same", name="conv7", trainable=True,
reuse=tf.AUTO_REUSE)
c8 = tf.layers.conv2d(c7, 16, 5, strides=1, activation=tf.nn.relu, padding="same", name="conv8", trainable=True,
reuse=tf.AUTO_REUSE)
c9 = tf.layers.conv2d(c8, 16, 5, strides=2, activation=tf.nn.relu, padding="same", name="conv9", trainable=True,
reuse=tf.AUTO_REUSE)
print(c9.shape)
# Lowest Convolutions
c10 = tf.layers.conv2d(c9, 32, 5, strides=1, activation=tf.nn.relu, padding="same", name="conv10", trainable=True,
reuse=tf.AUTO_REUSE)
c11 = tf.layers.conv2d(c10, 32, 5, strides=1, activation=tf.nn.relu, padding="same", name="conv11", trainable=True,
reuse=tf.AUTO_REUSE)
c12 = tf.layers.conv2d(c11, 32, 5, strides=1, activation=tf.nn.relu, padding="same", name="conv12", trainable=True,
reuse=tf.AUTO_REUSE)
print(c12.shape)
# UpConv Level 3
u1 = upsample2x(c12)
uc1 = tf.layers.conv2d(tf.concat([u1, c8], 3), 16, 5, strides=1, activation=tf.nn.relu, padding="same",
name="upconv1", trainable=True, reuse=tf.AUTO_REUSE)
uc2 = tf.layers.conv2d(uc1, 16, 5, strides=1, activation=tf.nn.relu, padding="same", name="upconv2",
trainable=True, reuse=tf.AUTO_REUSE)
uc3 = tf.layers.conv2d(uc2, 16, 5, strides=1, activation=tf.nn.relu, padding="same", name="upconv3",
trainable=True, reuse=tf.AUTO_REUSE)
print(uc3.shape)
# UpConv Level 2
u2 = upsample2x(uc3)
uc4 = tf.layers.conv2d(tf.concat([u2, c5], 3), 8, 5, strides=1, activation=tf.nn.relu, padding="same",
name="upconv4", trainable=True, reuse=tf.AUTO_REUSE)
uc5 = tf.layers.conv2d(uc4, 8, 5, strides=1, activation=tf.nn.relu, padding="same", name="upconv5",
trainable=True, reuse=tf.AUTO_REUSE)
uc6 = tf.layers.conv2d(uc5, 8, 5, strides=1, activation=tf.nn.relu, padding="same", name="upconv6",
trainable=True, reuse=tf.AUTO_REUSE)
print(uc6.shape)
# UpConv Level 1
u3 = upsample2x(uc6)
uc7 = tf.layers.conv2d(tf.concat([u3, c2], 3), 4, 5, strides=1, activation=tf.nn.relu, padding="same",
name="upconv7", trainable=True, reuse=tf.AUTO_REUSE)
uc8 = tf.layers.conv2d(uc7, 4, 5, strides=1, activation=tf.nn.relu, padding="same", name="upconv8",
trainable=True, reuse=tf.AUTO_REUSE)
uc9 = tf.layers.conv2d(uc8, 4, 5, strides=1, activation=tf.nn.relu, padding="same", name="upconv9",
trainable=True, reuse=tf.AUTO_REUSE)
print(uc9.shape)
# final Convolution
out = tf.layers.conv2d(uc9, 1, 5, strides=1, activation=None, padding="same", name="out_conv", trainable=True,
reuse=tf.AUTO_REUSE)
print(out.shape)
return out
def u_net(domain, input_fields, output_field, levels=2, filters=16, blocks_per_level=2, skip_combine='concat', training=False, trainable=True, reuse=None):
"""
Restrictions:
- 2D only
- Domain resolution must be multiple of 2**levels
:param skip_combine: 'concat'
:param blocks_per_level: number of residual blocks per level
:param filters: Number of convolutional filters
:type filters: int or tuple or list
:param levels: number of additional resolution levels, equals number of downsampling / upsampling operations
:param domain: the u-net is executed on this domain.
:type domain: Domain
:param input_fields: list of Fields to be passed to the network as input
:param output_field: determines sample points of the result
:param training: whether the network is executed in training or inference mode
:param trainable: whether the weights of the network are trainable
:param reuse: whether to reuse weights from previous unet calls
:return: Field sampled like output_field
"""
assert isinstance(domain, Domain)
assert isinstance(output_field, Field)
net_inputs = []
for input_field in input_fields:
assert isinstance(input_field, Field)
resampled = input_field.at(domain)
net_inputs.append(resampled)
y = CenteredGrid.sample(math.concat([math.to_float(grid.data) for grid in net_inputs], axis=-1), domain)
# --- Execute network ---
pad_width = sum([2 ** i for i in range(levels)])
y = y.padded([[0, pad_width]] * domain.rank)
resolutions = [y]
for level in range(levels):
level_filters = filters if isinstance(filters, int) else filters[level]
y = conv_layer(resolutions[0], level_filters, 2, strides=2, activation=tf.nn.relu, padding='valid', name='down_convolution_%d' % level, trainable=trainable, reuse=reuse)
for i in range(blocks_per_level):
y = residual_block(y, level_filters, name='down_res_block_%d_%d' % (level, i), training=training, trainable=trainable, reuse=reuse)
resolutions.insert(0, y)
y = resolutions.pop(0)
assert np.all(y.box.size == domain.box.size)
for level in range(levels):
y = math.upsample2x(y)
res_in = resolutions.pop(0)
res_in = res_in.at(y) # No resampling required, simply shaving off the top rows
if skip_combine == 'concat':
y = y.with_data(math.concat([y.data, res_in.data], axis=-1))
else:
raise NotImplementedError()
y = y + res_in
y = y.padded([[0, 1], [0, 1]])
if resolutions:
level_filters = filters if isinstance(filters, int) else reversed(filters)[level]
y = conv_layer(y, level_filters, kernel_size=2, activation=tf.nn.relu, padding='valid', name='up_convolution_%d' % level, trainable=trainable, reuse=reuse)
for i in range(blocks_per_level):
y = residual_block(y, level_filters, name='up_res_block_%d_%d' % (level, i), training=training, trainable=trainable, reuse=reuse)
else: # Last iteration
y = conv_layer(y, output_field.component_count, kernel_size=2, activation=None, padding='valid', name='up_convolution_%d' % level, trainable=trainable, reuse=reuse)
result = y.at(output_field)
return result