# Copyright 2022 Huawei Technologies Co., Ltd
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
# ============================================================================
import numpy as np
import mindspore.common.dtype as mstype
from mindspore import ops, nn, Tensor, Parameter
from mindspore.ops import operations as P
from mindspore.common.initializer import Zero
from .dft import dft2, idft2
from ...common.math import get_grid_2d
from ...utils.check_func import check_param_type
class SpectralConv2dDft(nn.Cell):
def __init__(self, in_channels, out_channels, modes1, modes2, column_resolution, raw_resolution,
compute_dtype=mstype.float16):
super().__init__()
self.in_channels = in_channels
self.out_channels = out_channels
self.modes1 = modes1
self.modes2 = modes2
self.column_resolution = column_resolution
self.raw_resolution = raw_resolution
self.compute_dtype = compute_dtype
self.scale = (1. / (in_channels * out_channels))
w_re1 = Tensor(
self.scale * np.random.rand(in_channels,
out_channels, modes1, modes2),
dtype=compute_dtype)
w_im1 = Tensor(
self.scale * np.random.rand(in_channels,
out_channels, modes1, modes2),
dtype=compute_dtype)
w_re2 = Tensor(
self.scale * np.random.rand(in_channels,
out_channels, modes1, modes2),
dtype=compute_dtype)
w_im2 = Tensor(
self.scale * np.random.rand(in_channels,
out_channels, modes1, modes2),
dtype=compute_dtype)
self.w_re1 = Parameter(w_re1, requires_grad=True)
self.w_im1 = Parameter(w_im1, requires_grad=True)
self.w_re2 = Parameter(w_re2, requires_grad=True)
self.w_im2 = Parameter(w_im2, requires_grad=True)
self.dft2_cell = dft2(shape=(column_resolution, raw_resolution), modes=(modes1, modes2),
compute_dtype=compute_dtype)
self.idft2_cell = idft2(shape=(column_resolution, raw_resolution), modes=(modes1, modes2),
compute_dtype=compute_dtype)
self.mat = Tensor(shape=(1, out_channels, column_resolution - 2 * modes1, modes2), dtype=compute_dtype,
init=Zero())
self.concat = ops.Concat(-2)
@staticmethod
def mul2d(inputs, weights):
weight = weights.expand_dims(0)
data = inputs.expand_dims(2)
out = weight * data
return out.sum(1)
def construct(self, x: Tensor):
x_re = x
x_im = ops.zeros_like(x_re)
x_ft_re, x_ft_im = self.dft2_cell((x_re, x_im))
out_ft_re1 = \
self.mul2d(x_ft_re[:, :, :self.modes1, :self.modes2], self.w_re1) \
- self.mul2d(x_ft_im[:, :, :self.modes1, :self.modes2], self.w_im1)
out_ft_im1 = \
self.mul2d(x_ft_re[:, :, :self.modes1, :self.modes2], self.w_im1) \
+ self.mul2d(x_ft_im[:, :, :self.modes1, :self.modes2], self.w_re1)
out_ft_re2 = \
self.mul2d(x_ft_re[:, :, -self.modes1:, :self.modes2], self.w_re2) \
- self.mul2d(x_ft_im[:, :, -self.modes1:, :self.modes2], self.w_im2)
out_ft_im2 = \
self.mul2d(x_ft_re[:, :, -self.modes1:, :self.modes2], self.w_im2) \
+ self.mul2d(x_ft_im[:, :, -self.modes1:, :self.modes2], self.w_re2)
batch_size = x.shape[0]
mat = self.mat.repeat(batch_size, 0)
out_re = self.concat((out_ft_re1, mat, out_ft_re2))
out_im = self.concat((out_ft_im1, mat, out_ft_im2))
x, _ = self.idft2_cell((out_re, out_im))
return x
class FNOBlock(nn.Cell):
def __init__(self, in_channels, out_channels, modes1, resolution=211, gelu=True, compute_dtype=mstype.float16):
super().__init__()
self.conv = SpectralConv2dDft(in_channels, out_channels, modes1, modes1, resolution, resolution,
compute_dtype=compute_dtype)
self.w = nn.Conv2d(in_channels, out_channels, 1,
weight_init='HeUniform').to_float(compute_dtype)
if gelu:
self.act = ops.GeLU()
else:
self.act = ops.Identity()
def construct(self, x):
return self.act(self.conv(x) + self.w(x))
[文档]class FNO2D(nn.Cell):
r"""
The 2-dimensional Fourier Neural Operator (FNO2D) contains a lifting layer,
multiple Fourier layers and a decoder layer.
The details can be found in `Fourier neural operator for parametric
partial differential equations <https://arxiv.org/pdf/2010.08895.pdf>`_.
Args:
in_channels (int): The number of channels in the input space.
out_channels (int): The number of channels in the output space.
resolution (int): The spatial resolution of the input.
modes (int): The number of low-frequency components to keep.
channels (int): The number of channels after dimension lifting of the input. Default: 20.
depths (int): The number of FNO layers. Default: 4.
mlp_ratio (int): The number of channels lifting ratio of the decoder layer. Default: 4.
compute_dtype (dtype.Number): The computation type of dense. Default mstype.float16.
Should be mstype.float16 or mstype.float32. mstype.float32 is recommended for the GPU backend,
mstype.float16 is recommended for the Ascend backend.
Inputs:
- **x** (Tensor) - Tensor of shape :math:`(batch\_size, resolution, resolution, in\_channels)`.
Outputs:
Tensor, the output of this FNO network.
- **output** (Tensor) -Tensor of shape :math:`(batch\_size, resolution, resolution, out\_channels)`.
Raises:
TypeError: If `in_channels` is not an int.
TypeError: If `out_channels` is not an int.
TypeError: If `resolution` is not an int.
TypeError: If `modes` is not an int.
ValueError: If `modes` is less than 1.
Supported Platforms:
``Ascend`` ``GPU``
Examples:
>>> import numpy as np
>>> from mindspore.common.initializer import initializer, Normal
>>> from mindflow.cell.neural_operators import FNO2D
>>> B, H, W, C = 32, 64, 64, 1
>>> input = initializer(Normal(), [B, H, W, C])
>>> net = FNO2D(in_channels=1, out_channels=1, resolution=64, modes=12)
>>> output = net(input)
>>> print(output.shape)
(32, 64, 64, 1)
"""
def __init__(self,
in_channels,
out_channels,
resolution,
modes,
channels=20,
depths=4,
mlp_ratio=4,
compute_dtype=mstype.float32):
super().__init__()
check_param_type(in_channels, "in_channels",
data_type=int, exclude_type=bool)
check_param_type(out_channels, "out_channels",
data_type=int, exclude_type=bool)
check_param_type(resolution, "resolution",
data_type=int, exclude_type=bool)
check_param_type(modes, "modes", data_type=int, exclude_type=bool)
if modes < 1:
raise ValueError(
"modes must at least 1, but got mode: {}".format(modes))
self.modes1 = modes
self.channels = channels
self.fc_channel = mlp_ratio * channels
self.fc0 = nn.Dense(in_channels + 2, self.channels,
has_bias=False).to_float(compute_dtype)
self.layers = depths
self.fno_seq = nn.SequentialCell()
for _ in range(self.layers - 1):
self.fno_seq.append(FNOBlock(self.channels, self.channels, modes1=self.modes1, resolution=resolution,
compute_dtype=compute_dtype))
self.fno_seq.append(
FNOBlock(self.channels, self.channels, self.modes1, resolution=resolution, gelu=False,
compute_dtype=compute_dtype))
self.fc1 = nn.Dense(self.channels, self.fc_channel,
has_bias=False).to_float(compute_dtype)
self.fc2 = nn.Dense(self.fc_channel, out_channels,
has_bias=False).to_float(compute_dtype)
self.grid = Tensor(get_grid_2d(resolution), dtype=mstype.float32)
self.concat = ops.Concat(axis=-1)
self.act = ops.GeLU()
def construct(self, x: Tensor):
batch_size = x.shape[0]
grid = self.grid.repeat(batch_size, axis=0)
x = P.Concat(-1)((x, grid))
x = self.fc0(x)
x = P.Transpose()(x, (0, 3, 1, 2))
x = self.fno_seq(x)
x = P.Transpose()(x, (0, 2, 3, 1))
x = self.fc1(x)
x = self.act(x)
output = self.fc2(x)
return output