-
Notifications
You must be signed in to change notification settings - Fork 19
/
10dpoisson-cube.py
257 lines (214 loc) · 9.49 KB
/
10dpoisson-cube.py
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
import numpy as np
import math, torch, generateData, time
import torch.nn.functional as F
from torch.optim.lr_scheduler import MultiStepLR, StepLR
import torch.nn as nn
import matplotlib.pyplot as plt
import sys, os
import writeSolution
from areaVolume import areaVolume
# Network structure
class RitzNet(torch.nn.Module):
def __init__(self, params):
super(RitzNet, self).__init__()
self.params = params
# self.linearIn = nn.Linear(self.params["d"], self.params["width"])
self.linear = nn.ModuleList()
for _ in range(params["depth"]):
self.linear.append(nn.Linear(self.params["width"], self.params["width"]))
self.linearOut = nn.Linear(self.params["width"], self.params["dd"])
def forward(self, x):
# x = torch.tanh(self.linearIn(x)) # Match dimension
for i in range(len(self.linear)//2):
x_temp = torch.tanh(self.linear[2*i](x))
x_temp = torch.tanh(self.linear[2*i+1](x_temp))
x = x_temp+x
return self.linearOut(x)
def initWeights(m):
if type(m) == nn.Linear:
torch.nn.init.xavier_normal_(m.weight)
torch.nn.init.zeros_(m.bias)
def preTrain(model,device,params,preOptimizer,preScheduler,fun):
model.train()
file = open("lossData.txt","w")
for step in range(params["preStep"]):
# The volume integral
data = torch.from_numpy(generateData.sampleFromDisk10(params["radius"],params["bodyBatch"])).float().to(device)
output = model(data)
target = fun(params["radius"],data)
loss = output-target
loss = torch.mean(loss*loss)
if step%params["writeStep"] == params["writeStep"]-1:
with torch.no_grad():
ref = exact(params["radius"],data)
error = errorFun(output,ref,params)
# print("Loss at Step %s is %s."%(step+1,loss.item()))
print("Error at Step %s is %s."%(step+1,error))
file.write(str(step+1)+" "+str(error)+"\n")
model.zero_grad()
loss.backward()
# Update the weights.
preOptimizer.step()
# preScheduler.step()
def train(model,device,params,optimizer,scheduler):
model.train()
data1 = torch.rand(params["bodyBatch"],params["d"]).float().to(device)
data2 = torch.rand(2*params["d"]*(params["bdryBatch"]//(2*params["d"])),params["d"]).float().to(device)
temp = params["bdryBatch"]//(2*params["d"])
for i in range(params["d"]):
data2[(2*i+0)*temp:(2*i+1)*temp,i] = 0.0
data2[(2*i+1)*temp:(2*i+2)*temp,i] = 1.0
x_shift = torch.from_numpy(np.eye(10)*params["diff"]).float().to(device)
data1_shift0 = data1+x_shift[0]
data1_shift1 = data1+x_shift[1]
data1_shift2 = data1+x_shift[2]
data1_shift3 = data1+x_shift[3]
data1_shift4 = data1+x_shift[4]
data1_shift5 = data1+x_shift[5]
data1_shift6 = data1+x_shift[6]
data1_shift7 = data1+x_shift[7]
data1_shift8 = data1+x_shift[8]
data1_shift9 = data1+x_shift[9]
for step in range(params["trainStep"]-params["preStep"]):
output1 = model(data1)
output1_shift0 = model(data1_shift0)
output1_shift1 = model(data1_shift1)
output1_shift2 = model(data1_shift2)
output1_shift3 = model(data1_shift3)
output1_shift4 = model(data1_shift4)
output1_shift5 = model(data1_shift5)
output1_shift6 = model(data1_shift6)
output1_shift7 = model(data1_shift7)
output1_shift8 = model(data1_shift8)
output1_shift9 = model(data1_shift9)
dfdx0 = (output1_shift0-output1)/params["diff"] # Use difference to approximate derivatives.
dfdx1 = (output1_shift1-output1)/params["diff"]
dfdx2 = (output1_shift2-output1)/params["diff"]
dfdx3 = (output1_shift3-output1)/params["diff"]
dfdx4 = (output1_shift4-output1)/params["diff"]
dfdx5 = (output1_shift5-output1)/params["diff"]
dfdx6 = (output1_shift6-output1)/params["diff"]
dfdx7 = (output1_shift7-output1)/params["diff"]
dfdx8 = (output1_shift8-output1)/params["diff"]
dfdx9 = (output1_shift9-output1)/params["diff"]
model.zero_grad()
# Loss function 1
fTerm = ffun(data1).to(device)
loss1 = torch.mean(0.5*(dfdx0*dfdx0 + dfdx1*dfdx1 + dfdx2*dfdx2 +\
dfdx3*dfdx3 + dfdx4*dfdx4 + dfdx5*dfdx5 + dfdx6*dfdx6 +\
dfdx7*dfdx7 + dfdx8*dfdx8 + dfdx9*dfdx9)-fTerm*output1)
# Loss function 2
output2 = model(data2)
target2 = exact(params["radius"],data2)
loss2 = torch.mean((output2-target2)*(output2-target2) * params["penalty"] *params["area"])
loss = loss1+loss2
if step%params["writeStep"] == params["writeStep"]-1:
with torch.no_grad():
target = exact(params["radius"],data1)
error = errorFun(output1,target,params)
# print("Loss at Step %s is %s."%(step+params["preStep"]+1,loss.item()))
print("Error at Step %s is %s."%(step+params["preStep"]+1,error))
file = open("lossData.txt","a")
file.write(str(step+params["preStep"]+1)+" "+str(error)+"\n")
if step%params["sampleStep"] == params["sampleStep"]-1:
data1 = torch.rand(params["bodyBatch"],params["d"]).float().to(device)
data2 = torch.rand(2*params["d"]*(params["bdryBatch"]//(2*params["d"])),params["d"]).float().to(device)
temp = params["bdryBatch"]//(2*params["d"])
for i in range(params["d"]):
data2[(2*i+0)*temp:(2*i+1)*temp,i] = 0.0
data2[(2*i+1)*temp:(2*i+2)*temp,i] = 1.0
data1_shift0 = data1+x_shift[0]
data1_shift1 = data1+x_shift[1]
data1_shift2 = data1+x_shift[2]
data1_shift3 = data1+x_shift[3]
data1_shift4 = data1+x_shift[4]
data1_shift5 = data1+x_shift[5]
data1_shift6 = data1+x_shift[6]
data1_shift7 = data1+x_shift[7]
data1_shift8 = data1+x_shift[8]
data1_shift9 = data1+x_shift[9]
if 10*(step+1)%params["trainStep"] == 0:
print("%s%% finished..."%(100*(step+1)//params["trainStep"]))
loss.backward()
optimizer.step()
scheduler.step()
def errorFun(output,target,params):
error = output-target
error = math.sqrt(torch.mean(error*error))
# Calculate the L2 norm error.
ref = math.sqrt(torch.mean(target*target))
return error/ref
def test(model,device,params):
numQuad = params["numQuad"]
data = torch.rand(numQuad,10).float().to(device)
output = model(data)
target = exact(params["radius"],data).to(device)
error = output-target
error = math.sqrt(torch.mean(error*error))
# Calculate the L2 norm error.
ref = math.sqrt(torch.mean(target*target))
return error/ref
def ffun(data):
# f = 0
return 0.0*torch.ones([data.shape[0],1],dtype=torch.float)
# f = 20
# return 20.0*torch.ones([data.shape[0],1],dtype=torch.float)
def exact(r,data):
# f = 20 ==> u = r^2-x^2-y^2-...
# output = r**2-torch.sum(data*data,dim=1)
# f = 0 ==> u = x1x2+x3x4+x5x6+...
output = data[:,0]*data[:,1] + data[:,2]*data[:,3] + data[:,4]*data[:,5] + \
data[:,6]*data[:,7] + data[:,8]*data[:,9]
return output.unsqueeze(1)
def rough(r,data):
# output = r**2-r*torch.sum(data*data,dim=1)**0.5
output = torch.zeros(data.shape[0],dtype=torch.float)
return output.unsqueeze(1)
def count_parameters(model):
return sum(p.numel() for p in model.parameters()) # if p.requires_grad
def main():
# Parameters
# torch.manual_seed(21)
device = torch.device("cuda:0" if torch.cuda.is_available() else "cpu")
params = dict()
params["radius"] = 1
params["d"] = 10 # 10D
params["dd"] = 1 # Scalar field
params["bodyBatch"] = 1024 # Batch size
params["bdryBatch"] = 2000 # Batch size for the boundary integral
params["lr"] = 0.016 # Learning rate
params["preLr"] = params["lr"] # Learning rate (Pre-training)
params["width"] = 10 # Width of layers
params["depth"] = 4 # Depth of the network: depth+2
params["numQuad"] = 40000 # Number of quadrature points for testing
params["trainStep"] = 50000
params["penalty"] = 500
params["preStep"] = 0
params["diff"] = 0.001
params["writeStep"] = 50
params["sampleStep"] = 10
params["area"] = 20
params["step_size"] = 5000
params["milestone"] = [5000,10000,20000,35000,48000]
params["gamma"] = 0.5
params["decay"] = 0.00001
startTime = time.time()
model = RitzNet(params).to(device)
model.apply(initWeights)
print("Generating network costs %s seconds."%(time.time()-startTime))
# torch.seed()
preOptimizer = torch.optim.Adam(model.parameters(),lr=params["preLr"])
optimizer = torch.optim.Adam(model.parameters(),lr=params["lr"],weight_decay=params["decay"])
# scheduler = StepLR(optimizer,step_size=params["step_size"],gamma=params["gamma"])
scheduler = MultiStepLR(optimizer,milestones=params["milestone"],gamma=params["gamma"])
startTime = time.time()
preTrain(model,device,params,preOptimizer,None,rough)
train(model,device,params,optimizer,scheduler)
print("Training costs %s seconds."%(time.time()-startTime))
model.eval()
testError = test(model,device,params)
print("The test error (of the last model) is %s."%testError)
print("The number of parameters is %s,"%count_parameters(model))
torch.save(model.state_dict(),"last_model.pt")
if __name__=="__main__":
main()