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darcy_flow_uno2d.py
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# Codes for section: Results on Darcy Flow Equation
import numpy as np
import torch
import torch.nn as nn
import torch.nn.functional as F
from torch.nn.parameter import Parameter
import math
import matplotlib.pyplot as plt
from integral_operators import *
import operator
from functools import reduce
from functools import partial
from timeit import default_timer
from utilities3 import *
from Adam import Adam
torch.manual_seed(0)
np.random.seed(0)
###############
# UNO^dagger achitechtures
###############
class UNO_9(nn.Module):
"""
The overall network. It contains 13 integral operator.
1. Lift the input to the desire channel dimension by self.fc, self.fc0 .
2. 5 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: Diffusion coefficient (a)
input shape: (batchsize, x=S, y=S, 1, 1)
output: the solution of the next timesteps
output shape: (batchsize, x=S, y=S, 1, 1)
Spatial Resulution = SxS
in_width = 3 ; [a(x,y),x,y]
with = Up-lifting dimension
pad = padding the domian for non-periodic input
factor = factor for scaling up/down the co-domain dimension at each integral operator
"""
def __init__(self, in_width, width,pad = 5, factor = 1):
super(UNO_9, self).__init__()
self.in_width = in_width # input channel
self.width = width
self.padding = pad # pad the domain if input is non-periodic
self.fc_n1 = nn.Linear(self.in_width, self.width//2)
self.fc0 = nn.Linear(self.width//2, self.width) # input channel is 3: (a(x, y), x, y)
self.conv0 = OperatorBlock_2D(self.width, 2*factor*self.width,40, 40, 18, 18)
self.conv1 = OperatorBlock_2D(2*factor*self.width, 4*factor*self.width, 20, 20, 8,8, Normalize = True)
self.conv2 = OperatorBlock_2D(4*factor*self.width, 4*factor*self.width, 20, 20,8,8)
self.conv4 = OperatorBlock_2D(4*factor*self.width, 2*factor*self.width, 40, 40,8,8, Normalize = True)
self.conv5 = OperatorBlock_2D(4*factor*self.width, self.width, 85, 85,18,18) # will be reshaped
self.fc1 = nn.Linear(2*self.width, 1*self.width)
self.fc2 = nn.Linear(1*self.width, 1)
def forward(self, x):
grid = self.get_grid(x.shape, x.device)
x = torch.cat((x, grid), dim=-1)
x_fc_1 = self.fc_n1(x)
x_fc_1 = F.gelu(x_fc_1)
x_fc0 = self.fc0(x_fc_1)
x_fc0 = F.gelu(x_fc0)
x_fc0 = x_fc0.permute(0, 3, 1, 2)
scale = math.ceil(x_fc0.shape[-1]/85)
x_fc0 = F.pad(x_fc0, [0,scale*self.padding, 0,scale*self.padding])
D1,D2 = x_fc0.shape[-2],x_fc0.shape[-1]
x_c0 = self.conv0(x_fc0,D1//2,D2//2)
x_c1 = self.conv1(x_c0,D1//4,D2//4)
x_c2 = self.conv2(x_c1,D1//4,D2//4)
x_c4 = self.conv4(x_c2 ,D1//2,D2//2)
x_c4 = torch.cat([x_c4, x_c0], dim=1)
x_c5 = self.conv5(x_c4,D1,D2)
x_c5 = torch.cat([x_c5, x_fc0], dim=1)
if self.padding!=0:
x_c5 = x_c5[..., :-scale*self.padding, :-scale*self.padding]
x_c5 = x_c5.permute(0, 2, 3, 1)
x_fc1 = self.fc1(x_c5)
x_fc1 = F.gelu(x_fc1)
x_out = self.fc2(x_fc1)
return x_out
def get_grid(self, shape, device):
batchsize, size_x, size_y = shape[0], shape[1], shape[2]
gridx = torch.tensor(np.linspace(0, 1, size_x), dtype=torch.float)
gridx = gridx.reshape(1, size_x, 1, 1).repeat([batchsize, 1, size_y, 1])
gridy = torch.tensor(np.linspace(0, 1, size_y), dtype=torch.float)
gridy = gridy.reshape(1, 1, size_y, 1).repeat([batchsize, size_x, 1, 1])
return torch.cat((gridx, gridy), dim=-1).to(device)
# For the following classes every parameters acts the same as UNO_P_13.
##UNO^dagger 11 layers
class UNO_11(nn.Module):
def __init__(self, in_width, width,pad = 5, factor = 1):
super(UNO_11, self).__init__()
self.in_width = in_width # input channel
self.width = width
self.padding = pad # pad the domain if input is non-periodic
self.fc_n1 = nn.Linear(self.in_width, self.width//2)
self.fc0 = nn.Linear(self.width//2, self.width) # input channel is 3: (a(x, y), x, y)
self.conv0 = OperatorBlock_2D(self.width, 2*factor*self.width,40, 40, 18, 18)
self.conv1 = OperatorBlock_2D(2*factor*self.width, 4*factor*self.width, 20, 20, 8,8, Normalize = True)
self.conv2 = OperatorBlock_2D(4*factor*self.width, 8*factor*self.width, 8, 8,3,3)
self.conv2_5 = OperatorBlock_2D(8*factor*self.width, 8*factor*self.width, 8, 8,3,3, Normalize = True, residual = True)
self.conv3 = OperatorBlock_2D(8*factor*self.width, 4*factor*self.width, 20, 20,3,3)
self.conv4 = OperatorBlock_2D(8*factor*self.width, 2*factor*self.width, 40, 40,8,8, Normalize = True)
self.conv5 = OperatorBlock_2D(4*factor*self.width, self.width, 85, 85,18,18) # will be reshaped
self.fc1 = nn.Linear(2*self.width, 1*self.width)
self.fc2 = nn.Linear(1*self.width, 1)
def forward(self, x):
grid = self.get_grid(x.shape, x.device)
x = torch.cat((x, grid), dim=-1)
x_fc_1 = self.fc_n1(x)
x_fc_1 = F.gelu(x_fc_1)
x_fc0 = self.fc0(x_fc_1)
x_fc0 = F.gelu(x_fc0)
x_fc0 = x_fc0.permute(0, 3, 1, 2)
scale = math.ceil(x_fc0.shape[-1]/85)
x_fc0 = F.pad(x_fc0, [0,scale*self.padding, 0,scale*self.padding])
D1,D2 = x_fc0.shape[-2],x_fc0.shape[-1]
x_c0 = self.conv0(x_fc0,D1//2,D2//2)
x_c1 = self.conv1(x_c0,D1//4,D2//4)
x_c2 = self.conv2(x_c1,D1//8,D2//8)
x_c2_5 = self.conv2_5(x_c2,D1//8,D2//8)
x_c3 = self.conv3(x_c2_5 ,D1//4,D2//4)
x_c3 = torch.cat([x_c3, x_c1], dim=1)
x_c4 = self.conv4(x_c3 ,D1//2,D2//2)
x_c4 = torch.cat([x_c4, x_c0], dim=1)
x_c5 = self.conv5(x_c4,D1,D2)
x_c5 = torch.cat([x_c5, x_fc0], dim=1)
if self.padding!=0:
x_c5 = x_c5[..., :-scale*self.padding, :-scale*self.padding]
x_c5 = x_c5.permute(0, 2, 3, 1)
x_fc1 = self.fc1(x_c5)
x_fc1 = F.gelu(x_fc1)
#x_fc1 = torch.cat([x_fc1, x_fc_1], dim=3)
x_out = self.fc2(x_fc1)
return x_out
def get_grid(self, shape, device):
batchsize, size_x, size_y = shape[0], shape[1], shape[2]
gridx = torch.tensor(np.linspace(0, 1, size_x), dtype=torch.float)
gridx = gridx.reshape(1, size_x, 1, 1).repeat([batchsize, 1, size_y, 1])
gridy = torch.tensor(np.linspace(0, 1, size_y), dtype=torch.float)
gridy = gridy.reshape(1, 1, size_y, 1).repeat([batchsize, size_x, 1, 1])
return torch.cat((gridx, gridy), dim=-1).to(device)