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############################
'''
The implement codes of FNO were taken and modified from: https://github.com/neuraloperator/physics_informed
'''
import numpy as np
import torch
import torch.nn as nn
from onescience.utils.pdenneval.pino_utils import add_padding, remove_padding, add_padding2, remove_padding2, add_padding3, remove_padding3, _get_act
@torch.jit.script
def compl_mul1d(a: torch.Tensor, b: torch.Tensor) -> torch.Tensor:
# (batch, in_channel, x ), (in_channel, out_channel, x) -> (batch, out_channel, x)
res = torch.einsum("bix,iox->box", a, b)
return res
@torch.jit.script
def compl_mul2d(a: torch.Tensor, b: torch.Tensor) -> torch.Tensor:
# (batch, in_channel, x,y,t ), (in_channel, out_channel, x,y,t) -> (batch, out_channel, x,y,t)
res = torch.einsum("bixy,ioxy->boxy", a, b)
return res
@torch.jit.script
def compl_mul3d(a: torch.Tensor, b: torch.Tensor) -> torch.Tensor:
res = torch.einsum("bixyz,ioxyz->boxyz", a, b)
return res
################################################################
# 1d fourier layer
################################################################
class SpectralConv1d(nn.Module):
def __init__(self, in_channels, out_channels, modes1):
super(SpectralConv1d, self).__init__()
"""
1D Fourier layer. It does FFT, linear transform, and Inverse FFT.
"""
self.in_channels = in_channels
self.out_channels = out_channels
# Number of Fourier modes to multiply, at most floor(N/2) + 1
self.modes1 = modes1
self.scale = (1 / (in_channels*out_channels))
self.weights1 = nn.Parameter(
self.scale * torch.rand(in_channels, out_channels, self.modes1, dtype=torch.cfloat))
def forward(self, x):
batchsize = x.shape[0]
# Compute Fourier coeffcients up to factor of e^(- something constant)
x_ft = torch.fft.rfftn(x, dim=[2])
# Multiply relevant Fourier modes
out_ft = torch.zeros(batchsize, self.in_channels, x.size(-1)//2 + 1, device=x.device, dtype=torch.cfloat)
out_ft[:, :, :self.modes1] = compl_mul1d(x_ft[:, :, :self.modes1], self.weights1)
# Return to physical space
x = torch.fft.irfftn(out_ft, s=[x.size(-1)], dim=[2])
return x
################################################################
# 2d fourier layer
################################################################
class SpectralConv2d(nn.Module):
def __init__(self, in_channels, out_channels, modes1, modes2):
super(SpectralConv2d, self).__init__()
self.in_channels = in_channels
self.out_channels = out_channels
# Number of Fourier modes to multiply, at most floor(N/2) + 1
self.modes1 = modes1
self.modes2 = modes2
self.scale = (1 / (in_channels * out_channels))
self.weights1 = nn.Parameter(
self.scale * torch.rand(in_channels, out_channels, self.modes1, self.modes2, dtype=torch.cfloat))
self.weights2 = nn.Parameter(
self.scale * torch.rand(in_channels, out_channels, self.modes1, self.modes2, dtype=torch.cfloat))
def forward(self, x):
batchsize = x.shape[0]
size1 = x.shape[-2]
size2 = x.shape[-1]
# Compute Fourier coeffcients up to factor of e^(- something constant)
x_ft = torch.fft.rfftn(x, dim=[2, 3])
# Multiply relevant Fourier modes
out_ft = torch.zeros(batchsize, self.out_channels, x.size(-2), x.size(-1) // 2 + 1, device=x.device,
dtype=torch.cfloat)
out_ft[:, :, :self.modes1, :self.modes2] = \
compl_mul2d(x_ft[:, :, :self.modes1, :self.modes2], self.weights1)
out_ft[:, :, -self.modes1:, :self.modes2] = \
compl_mul2d(x_ft[:, :, -self.modes1:, :self.modes2], self.weights2)
# Return to physical space
x = torch.fft.irfftn(out_ft, s=(x.size(-2), x.size(-1)), dim=[2, 3])
return x
class SpectralConv3d(nn.Module):
def __init__(self, in_channels, out_channels, modes1, modes2, modes3):
super(SpectralConv3d, self).__init__()
self.in_channels = in_channels
self.out_channels = out_channels
self.modes1 = modes1 #Number of Fourier modes to multiply, at most floor(N/2) + 1
self.modes2 = modes2
self.modes3 = modes3
self.scale = (1 / (in_channels * out_channels))
self.weights1 = nn.Parameter(self.scale * torch.rand(in_channels, out_channels, self.modes1, self.modes2, self.modes3, dtype=torch.cfloat))
self.weights2 = nn.Parameter(self.scale * torch.rand(in_channels, out_channels, self.modes1, self.modes2, self.modes3, dtype=torch.cfloat))
self.weights3 = nn.Parameter(self.scale * torch.rand(in_channels, out_channels, self.modes1, self.modes2, self.modes3, dtype=torch.cfloat))
self.weights4 = nn.Parameter(self.scale * torch.rand(in_channels, out_channels, self.modes1, self.modes2, self.modes3, dtype=torch.cfloat))
def forward(self, x):
batchsize = x.shape[0]
# Compute Fourier coeffcients up to factor of e^(- something constant)
x_ft = torch.fft.rfftn(x, dim=[2,3,4])
z_dim = min(x_ft.shape[4], self.modes3)
# Multiply relevant Fourier modes
out_ft = torch.zeros(batchsize, self.out_channels, x_ft.shape[2], x_ft.shape[3], self.modes3, device=x.device, dtype=torch.cfloat)
# if x_ft.shape[4] > self.modes3, truncate; if x_ft.shape[4] < self.modes3, add zero padding
coeff = torch.zeros(batchsize, self.in_channels, self.modes1, self.modes2, self.modes3, device=x.device, dtype=torch.cfloat)
coeff[..., :z_dim] = x_ft[:, :, :self.modes1, :self.modes2, :z_dim]
out_ft[:, :, :self.modes1, :self.modes2, :] = compl_mul3d(coeff, self.weights1)
coeff = torch.zeros(batchsize, self.in_channels, self.modes1, self.modes2, self.modes3, device=x.device, dtype=torch.cfloat)
coeff[..., :z_dim] = x_ft[:, :, -self.modes1:, :self.modes2, :z_dim]
out_ft[:, :, -self.modes1:, :self.modes2, :] = compl_mul3d(coeff, self.weights2)
coeff = torch.zeros(batchsize, self.in_channels, self.modes1, self.modes2, self.modes3, device=x.device, dtype=torch.cfloat)
coeff[..., :z_dim] = x_ft[:, :, :self.modes1, -self.modes2:, :z_dim]
out_ft[:, :, :self.modes1, -self.modes2:, :] = compl_mul3d(coeff, self.weights3)
coeff = torch.zeros(batchsize, self.in_channels, self.modes1, self.modes2, self.modes3, device=x.device, dtype=torch.cfloat)
coeff[..., :z_dim] = x_ft[:, :, -self.modes1:, -self.modes2:, :z_dim]
out_ft[:, :, -self.modes1:, -self.modes2:, :] = compl_mul3d(coeff, self.weights4)
#Return to physical space
x = torch.fft.irfftn(out_ft, s=(x.size(2), x.size(3), x.size(4)), dim=[2,3,4])
return x
class FourierBlock(nn.Module):
def __init__(self, in_channels, out_channels, modes1, modes2, modes3, act='tanh'):
super(FourierBlock, self).__init__()
self.in_channel = in_channels
self.out_channel = out_channels
self.speconv = SpectralConv3d(in_channels, out_channels, modes1, modes2, modes3)
self.linear = nn.Conv1d(in_channels, out_channels, 1)
if act in ['tanh','gelu','none']:
self.act=_get_act(act)
else:
raise ValueError(f'{act} is not supported')
def forward(self, x):
'''
input x: (batchsize, channel width, x_grid, y_grid, t_grid)
'''
x1 = self.speconv(x)
x2 = self.linear(x.view(x.shape[0], self.in_channel, -1))
out = x1 + x2.view(x.shape[0], self.out_channel, x.shape[2], x.shape[3], x.shape[4])
if self.act is not None:
out = self.act(out)
return out
class FNO1d(nn.Module):
def __init__(self,
modes, width=32,
layers=None,
fc_dim=128,
in_dim=2, out_dim=1,
act='relu',
pad_ratio=[0.,0.1]):
super(FNO1d, self).__init__()
"""
The overall network. It contains several layers of the Fourier layer.
1. Lift the input to the desire channel dimension by self.fc0 .
2. 4 layers of the integral operators u' = (W + K)(u).
W defined by self.w; K defined by self.conv .
3. Project from the channel space to the output space by self.fc1 and self.fc2 .
input: the solution of the initial condition and location (a(x), x)
input shape: (batchsize, x=s, c=2)
output: the solution of a later timestep
output shape: (batchsize, x=s, c=1)
"""
self.modes1 = modes
self.width = width
self.pad_ratio = pad_ratio
if layers is None:
layers = [width] * 4
self.fc0 = nn.Linear(in_dim, layers[0]) # input channel is 2: (a(x), x)
self.sp_convs = nn.ModuleList([SpectralConv1d(
in_size, out_size, num_modes) for in_size, out_size, num_modes in zip(layers, layers[1:], self.modes1)])
self.ws = nn.ModuleList([nn.Conv1d(in_size, out_size, 1)
for in_size, out_size in zip(layers, layers[1:])])
self.fc1 = nn.Linear(layers[-1], fc_dim)
self.fc2 = nn.Linear(fc_dim, out_dim)
self.act = _get_act(act)
def forward(self, x):
length = len(self.ws)
size_1= x.shape[1]
if max(self.pad_ratio) > 0:
num_pad = [round(size_1 * i) for i in self.pad_ratio]
else:
num_pad = [0., 0.]
x = self.fc0(x)
x = x.permute(0, 2, 1)
x = add_padding(x,num_pad)
for i, (speconv, w) in enumerate(zip(self.sp_convs, self.ws)):
x1 = speconv(x)
x2 = w(x)
x = x1 + x2
if i != length - 1:
x = self.act(x)
x = remove_padding(x,num_pad)
x = x.permute(0, 2, 1)
x = self.fc1(x)
x = self.act(x)
x = self.fc2(x)
return x
class FNO2d(nn.Module):
def __init__(self, modes1, modes2,
width=64, fc_dim=128,
layers=None,
in_dim=3, out_dim=1,
act='gelu',
pad_ratio=[0., 0.1]):
super(FNO2d, self).__init__()
"""
Args:
- modes1: list of int, number of modes in first dimension in each layer
- modes2: list of int, number of modes in second dimension in each layer
- width: int, optional, if layers is None, it will be initialized as [width] * [len(modes1) + 1]
- in_dim: number of input channels
- out_dim: number of output channels
- act: activation function, {tanh, gelu, relu, leaky_relu}, default: gelu
- pad_ratio: list of float, or float; portion of domain to be extended. If float, paddings are added to the right.
If list, paddings are added to both sides. pad_ratio[0] pads left, pad_ratio[1] pads right.
"""
if isinstance(pad_ratio, float):
pad_ratio = [pad_ratio, pad_ratio]
else:
assert len(pad_ratio) == 2, 'Cannot add padding in more than 2 directions'
self.modes1 = modes1
self.modes2 = modes2
self.pad_ratio = pad_ratio
# input channel is 3: (a(x, y), x, y)
if layers is None:
self.layers = [width] * (len(modes1) + 1)
else:
self.layers = layers
self.fc0 = nn.Linear(in_dim, self.layers[0])
self.sp_convs = nn.ModuleList([SpectralConv2d(
in_size, out_size, mode1_num, mode2_num)
for in_size, out_size, mode1_num, mode2_num
in zip(self.layers, self.layers[1:], self.modes1, self.modes2)])
self.ws = nn.ModuleList([nn.Conv1d(in_size, out_size, 1)
for in_size, out_size in zip(self.layers, self.layers[1:])])
self.fc1 = nn.Linear(self.layers[-1], fc_dim)
self.fc2 = nn.Linear(fc_dim, self.layers[-1])
self.fc3 = nn.Linear(self.layers[-1], out_dim)
self.act = _get_act(act)
def forward(self, x):
'''
Args:
- x : (batch size, x_grid, y_grid, 2)
Returns:
- x: (batch size, x_grid, y_grid, 1)
'''
size_1, size_2 = x.shape[1], x.shape[2]
if max(self.pad_ratio) > 0:
num_pad1 = [round(i * size_1) for i in self.pad_ratio]
num_pad2 = [round(i * size_2) for i in self.pad_ratio]
else:
num_pad1 = num_pad2 = [0.,0.]
length = len(self.ws)
batchsize = x.shape[0]
x = self.fc0(x)
x = x.permute(0, 3, 1, 2) # B, C, X, Y
x = add_padding2(x, num_pad1, num_pad2)
size_x, size_y = x.shape[-2], x.shape[-1]
for i, (speconv, w) in enumerate(zip(self.sp_convs, self.ws)):
x1 = speconv(x)
x2 = w(x.view(batchsize, self.layers[i], -1)).view(batchsize, self.layers[i+1], size_x, size_y)
x = x1 + x2
if i != length - 1:
x = self.act(x)
x = remove_padding2(x, num_pad1, num_pad2)
x = x.permute(0, 2, 3, 1)
x = self.fc1(x)
x = self.act(x)
x = self.fc2(x)
x = self.act(x)
x = self.fc3(x)
return x
class FNO3d(nn.Module):
def __init__(self,
modes1, modes2, modes3,
width=16,
fc_dim=128,
layers=None,
in_dim=4, out_dim=1,
act='gelu',
pad_ratio=[0., 0.05]):
'''
Args:
modes1: list of int, first dimension maximal modes for each layer
modes2: list of int, second dimension maximal modes for each layer
modes3: list of int, third dimension maximal modes for each layer
layers: list of int, channels for each layer
fc_dim: dimension of fully connected layers
in_dim: int, input dimension
out_dim: int, output dimension
act: {tanh, gelu, relu, leaky_relu}, activation function
pad_ratio: the ratio of the extended domain
'''
super(FNO3d, self).__init__()
if isinstance(pad_ratio, float):
pad_ratio = [pad_ratio, pad_ratio]
else:
assert len(pad_ratio) == 2, 'Cannot add padding in more than 2 directions.'
self.pad_ratio = pad_ratio
self.modes1 = modes1
self.modes2 = modes2
self.modes3 = modes3
self.pad_ratio = pad_ratio
if layers is None:
self.layers = [width] * 4
else:
self.layers = layers
self.fc0 = nn.Linear(in_dim, self.layers[0])
self.sp_convs = nn.ModuleList([SpectralConv3d(
in_size, out_size, mode1_num, mode2_num, mode3_num)
for in_size, out_size, mode1_num, mode2_num, mode3_num
in zip(self.layers, self.layers[1:], self.modes1, self.modes2, self.modes3)])
self.ws = nn.ModuleList([nn.Conv1d(in_size, out_size, 1)
for in_size, out_size in zip(self.layers, self.layers[1:])])
self.fc1 = nn.Linear(self.layers[-1], fc_dim)
self.fc2 = nn.Linear(fc_dim, out_dim)
self.act = _get_act(act)
def forward(self, x):
'''
Args:
x: (batchsize, x_grid, y_grid, t_grid, 3)
Returns:
u: (batchsize, x_grid, y_grid, t_grid, 1)
'''
size_x,size_y,size_z = x.shape[1],x.shape[2],x.shape[3]
if max(self.pad_ratio) > 0:
num_pad1 = [round(size_x * i) for i in self.pad_ratio]
num_pad2 = [round(size_y * i) for i in self.pad_ratio]
num_pad3 = [round(size_z * i) for i in self.pad_ratio]
else:
num_pad1 = num_pad2 = num_pad3 = [0., 0.]
length = len(self.ws)
batchsize = x.shape[0]
x = self.fc0(x)
x = x.permute(0, 4, 1, 2, 3)
x = add_padding3(x, num_pad1,num_pad2,num_pad3)
size_x, size_y, size_z = x.shape[-3], x.shape[-2], x.shape[-1]
for i, (speconv, w) in enumerate(zip(self.sp_convs, self.ws)):
x1 = speconv(x)
x2 = w(x.view(batchsize, self.layers[i], -1)).view(batchsize, self.layers[i+1], size_x, size_y, size_z)
x = x1 + x2
if i != length - 1:
x = self.act(x)
x = remove_padding3(x, num_pad1,num_pad2,num_pad3)
x = x.permute(0, 2, 3, 4, 1)
x = self.fc1(x)
x = self.act(x)
x = self.fc2(x)
return x
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