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navier_stokes_uno2d.py
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# Codes for section: Results on Navier Stocks Equation (2D)
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 model more aggressive domian contraction and expansion (factor of 1/2)
class UNO_P(nn.Module):
def __init__(self, in_width, width, pad=0, factor=1):
super(UNO_P, self).__init__()
"""
The overall network. It contains 7 integral operator.
1. Lift the input to the desire channel dimension by self.fc, self.fc0 .
2. 7 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 first 10 timesteps (u(1), ..., u(10)).
input shape: (batchsize, x=S, y=S, t=10)
output: the solution of the next timesteps
output shape: (batchsize, x=S, y=S, t=1)
Here SxS is the spatial resolution
in_width = 12 (10 input time steps + (x,y) location)
with = uplifting dimension
pad = padding the domian for non-periodic input
factor = factor for scaling up/down the co-domain dimension at each integral operator
"""
self.in_width = in_width # input channel
self.width = width
self.padding = pad # pad the domain if input is non-periodic
self.fc = 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.L0 = OperatorBlock_2D(self.width, 2 * factor * self.width, 32, 32, 14, 14)
self.L1 = OperatorBlock_2D(
2 * factor * self.width, 4 * factor * self.width, 16, 16, 6, 6
)
self.L2 = OperatorBlock_2D(
4 * factor * self.width, 8 * factor * self.width, 8, 8, 3, 3
)
self.L3 = OperatorBlock_2D(
8 * factor * self.width, 8 * factor * self.width, 8, 8, 3, 3
)
self.L4 = OperatorBlock_2D(
8 * factor * self.width, 4 * factor * self.width, 16, 16, 3, 3
)
self.L5 = OperatorBlock_2D(
8 * factor * self.width, 2 * factor * self.width, 32, 32, 6, 6
)
self.L6 = OperatorBlock_2D(
4 * factor * self.width, self.width, 64, 64, 14, 14
) # will be reshaped
self.fc1 = nn.Linear(2 * self.width, 3 * self.width)
self.fc2 = nn.Linear(3 * self.width + self.width // 2, 1)
def forward(self, x):
grid = self.get_grid(x.shape, x.device)
x = torch.cat((x, grid), dim=-1)
x_fc = self.fc(x)
x_fc = F.gelu(x_fc)
x_fc0 = self.fc0(x_fc)
x_fc0 = F.gelu(x_fc0)
x_fc0 = x_fc0.permute(0, 3, 1, 2)
x_fc0 = F.pad(x_fc0, [self.padding, self.padding, self.padding, self.padding])
D1, D2 = x_fc0.shape[-2], x_fc0.shape[-1]
x_c0 = self.L0(x_fc0, D1 // 2, D2 // 2)
x_c1 = self.L1(x_c0, D1 // 4, D2 // 4)
x_c2 = self.L2(x_c1, D1 // 8, D2 // 8)
x_c3 = self.L3(x_c2, D1 // 8, D2 // 8)
x_c4 = self.L4(x_c3, D1 // 4, D2 // 4)
x_c4 = torch.cat([x_c4, x_c1], dim=1)
x_c5 = self.L5(x_c4, D1 // 2, D2 // 2)
x_c5 = torch.cat([x_c5, x_c0], dim=1)
x_c6 = self.L6(x_c5, D1, D2)
x_c6 = torch.cat([x_c6, x_fc0], dim=1)
if self.padding != 0:
x_c6 = x_c6[..., self.padding : -self.padding, self.padding : -self.padding]
x_c6 = x_c6.permute(0, 2, 3, 1)
x_fc1 = self.fc1(x_c6)
x_fc1 = F.gelu(x_fc1)
x_fc1 = torch.cat([x_fc1, x_fc], 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, 2 * np.pi, 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, 2 * np.pi, size_y), dtype=torch.float)
gridy = gridy.reshape(1, 1, size_y, 1).repeat([batchsize, size_x, 1, 1])
return torch.cat(
(torch.sin(gridx), torch.sin(gridy), torch.cos(gridx), torch.cos(gridy)),
dim=-1,
).to(device)
#####
# UNO model
# it has less aggressive scaling factors for domains and co-domains.
# ####
class UNO(nn.Module):
def __init__(self, in_width, width, pad=0, factor=3 / 4):
super(UNO, self).__init__()
self.in_width = in_width # input channel
self.width = width
self.factor = factor
self.padding = pad
self.fc = 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.L0 = OperatorBlock_2D(self.width, 2 * factor * self.width, 48, 48, 22, 22)
self.L1 = OperatorBlock_2D(
2 * factor * self.width, 4 * factor * self.width, 32, 32, 14, 14
)
self.L2 = OperatorBlock_2D(
4 * factor * self.width, 8 * factor * self.width, 16, 16, 6, 6
)
self.L3 = OperatorBlock_2D(
8 * factor * self.width, 8 * factor * self.width, 16, 16, 6, 6
)
self.L4 = OperatorBlock_2D(
8 * factor * self.width, 4 * factor * self.width, 32, 32, 6, 6
)
self.L5 = OperatorBlock_2D(
8 * factor * self.width, 2 * factor * self.width, 48, 48, 14, 14
)
self.L6 = OperatorBlock_2D(
4 * factor * self.width, self.width, 64, 64, 22, 22
) # will be reshaped
self.fc1 = nn.Linear(2 * self.width, 4 * self.width)
self.fc2 = nn.Linear(4 * self.width, 1)
def forward(self, x):
grid = self.get_grid(x.shape, x.device)
x = torch.cat((x, grid), dim=-1)
x_fc = self.fc(x)
x_fc = F.gelu(x_fc)
x_fc0 = self.fc0(x_fc)
x_fc0 = F.gelu(x_fc0)
x_fc0 = x_fc0.permute(0, 3, 1, 2)
x_fc0 = F.pad(x_fc0, [self.padding, self.padding, self.padding, self.padding])
D1, D2 = x_fc0.shape[-2], x_fc0.shape[-1]
x_c0 = self.L0(x_fc0, int(D1 * self.factor), int(D2 * self.factor))
x_c1 = self.L1(x_c0, D1 // 2, D2 // 2)
x_c2 = self.L2(x_c1, D1 // 4, D2 // 4)
x_c3 = self.L3(x_c2, D1 // 4, D2 // 4)
x_c4 = self.L4(x_c3, D1 // 2, D2 // 2)
x_c4 = torch.cat([x_c4, x_c1], dim=1)
x_c5 = self.L5(x_c4, int(D1 * self.factor), int(D2 * self.factor))
x_c5 = torch.cat([x_c5, x_c0], dim=1)
x_c6 = self.L6(x_c5, D1, D2)
x_c6 = torch.cat([x_c6, x_fc0], dim=1)
if self.padding != 0:
x_c6 = x_c6[..., : -self.padding, : -self.padding]
x_c6 = x_c6.permute(0, 2, 3, 1)
x_fc1 = self.fc1(x_c6)
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, 2 * np.pi, 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, 2 * np.pi, size_y), dtype=torch.float)
gridy = gridy.reshape(1, 1, size_y, 1).repeat([batchsize, size_x, 1, 1])
return torch.cat(
(torch.sin(gridx), torch.sin(gridy), torch.cos(gridx), torch.cos(gridy)),
dim=-1,
).to(device)
###
# UNO for high resolution (256x256) navier stocks simulations
###
class UNO_S256(nn.Module):
def __init__(self, in_width, width, pad=0, factor=1):
super(UNO_S256, 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 = nn.Linear(self.in_width, 16)
self.fc0 = nn.Linear(16, self.width) # input channel is 3: (a(x, y), x, y)
self.L0 = OperatorBlock_2D(self.width, 2 * factor * self.width, 64, 64, 32, 33)
self.L1 = OperatorBlock_2D(
2 * factor * self.width, 4 * factor * self.width, 16, 16, 8, 9
)
self.L2 = OperatorBlock_2D(
4 * factor * self.width, 8 * factor * self.width, 8, 8, 4, 5
)
self.L3 = OperatorBlock_2D(
8 * factor * self.width, 8 * factor * self.width, 8, 8, 4, 5
)
self.L4 = OperatorBlock_2D(
8 * factor * self.width, 4 * factor * self.width, 16, 16, 4, 5
)
self.L5 = OperatorBlock_2D(
8 * factor * self.width, 2 * factor * self.width, 64, 64, 8, 9
)
self.L6 = OperatorBlock_2D(
4 * factor * self.width, self.width, 256, 256, 32, 32
) # will be reshaped
self.fc1 = nn.Linear(2 * self.width, 3 * self.width)
self.fc2 = nn.Linear(3 * self.width + 16, 1)
def forward(self, x):
grid = self.get_grid(x.shape, x.device)
x = torch.cat((x, grid), dim=-1)
x_fc = self.fc(x)
x_fc = F.gelu(x_fc)
x_fc0 = self.fc0(x_fc)
x_fc0 = F.gelu(x_fc0)
x_fc0 = x_fc0.permute(0, 3, 1, 2)
x_fc0 = F.pad(x_fc0, [self.padding, self.padding, self.padding, self.padding])
D1, D2 = x_fc0.shape[-2], x_fc0.shape[-1]
x_c0 = self.L0(x_fc0, D1 // 4, D2 // 4)
x_c1 = self.L1(x_c0, D1 // 16, D2 // 16)
x_c2 = self.L2(x_c1, D1 // 32, D2 // 32)
x_c3 = self.L3(x_c2, D1 // 32, D2 // 32)
x_c4 = self.L4(x_c3, D1 // 16, D2 // 16)
x_c4 = torch.cat([x_c4, x_c1], dim=1)
x_c5 = self.L5(x_c4, D1 // 4, D2 // 4)
x_c5 = torch.cat([x_c5, x_c0], dim=1)
x_c6 = self.L6(x_c5, D1, D2)
# print(x.shape)
x_c6 = torch.cat([x_c6, x_fc0], dim=1)
if self.padding != 0:
x_c6 = x_c6[..., self.padding : -self.padding, self.padding : -self.padding]
x_c6 = x_c6.permute(0, 2, 3, 1)
x_fc1 = self.fc1(x_c6)
x_fc1 = F.gelu(x_fc1)
x_fc1 = torch.cat([x_fc1, x_fc], 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, 2 * np.pi, 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, 2 * np.pi, size_y), dtype=torch.float)
gridy = gridy.reshape(1, 1, size_y, 1).repeat([batchsize, size_x, 1, 1])
return torch.cat(
(torch.sin(gridx), torch.sin(gridy), torch.cos(gridx), torch.cos(gridy)),
dim=-1,
).to(device)