-
Notifications
You must be signed in to change notification settings - Fork 6
/
1d_reaction_region_optimization.py
209 lines (170 loc) · 8.06 KB
/
1d_reaction_region_optimization.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
import time
import os
import torch
import torch.nn as nn
import matplotlib.pyplot as plt
import random
from torch.optim import LBFGS
from tqdm import tqdm
import argparse
from util import *
from model_dict import get_model
seed = 0
np.random.seed(seed)
random.seed(seed)
torch.manual_seed(seed)
torch.cuda.manual_seed(seed)
parser = argparse.ArgumentParser('Training Region Optimization')
parser.add_argument('--model', type=str, default='pinn')
parser.add_argument('--device', type=str, default='cuda:0')
parser.add_argument('--initial_region', type=float, default=1e-4)
parser.add_argument('--sample_num', type=int, default=1)
parser.add_argument('--past_iterations', type=int, default=10)
args = parser.parse_args()
device = args.device
res, b_left, b_right, b_upper, b_lower = get_data([0, 2 * np.pi], [0, 1], 101, 101)
res_test, _, _, _, _ = get_data([0, 2 * np.pi], [0, 1], 101, 101)
if args.model == 'PINNsFormer' or args.model == 'PINNsFormer_Enc_Only':
res = make_time_sequence(res, num_step=5, step=1e-4)
b_left = make_time_sequence(b_left, num_step=5, step=1e-4)
b_right = make_time_sequence(b_right, num_step=5, step=1e-4)
b_upper = make_time_sequence(b_upper, num_step=5, step=1e-4)
b_lower = make_time_sequence(b_lower, num_step=5, step=1e-4)
res = torch.tensor(res, dtype=torch.float32, requires_grad=True).to(device)
b_left = torch.tensor(b_left, dtype=torch.float32, requires_grad=True).to(device)
b_right = torch.tensor(b_right, dtype=torch.float32, requires_grad=True).to(device)
b_upper = torch.tensor(b_upper, dtype=torch.float32, requires_grad=True).to(device)
b_lower = torch.tensor(b_lower, dtype=torch.float32, requires_grad=True).to(device)
x_res, t_res = res[:, ..., 0:1], res[:, ..., 1:2]
x_left, t_left = b_left[:, ..., 0:1], b_left[:, ..., 1:2]
x_right, t_right = b_right[:, ..., 0:1], b_right[:, ..., 1:2]
x_upper, t_upper = b_upper[:, ..., 0:1], b_upper[:, ..., 1:2]
x_lower, t_lower = b_lower[:, ..., 0:1], b_lower[:, ..., 1:2]
def init_weights(m):
if isinstance(m, nn.Linear):
torch.nn.init.xavier_uniform(m.weight)
m.bias.data.fill_(0.01)
if args.model == 'KAN':
model = get_model(args).Model(width=[2, 5, 1], grid=5, k=3, grid_eps=1.0, \
noise_scale_base=0.25, device=device).to(device)
elif args.model == 'QRes':
model = get_model(args).Model(in_dim=2, hidden_dim=256, out_dim=1, num_layer=2).to(device)
model.apply(init_weights)
elif args.model == 'PINNsFormer' or args.model == 'PINNsFormer_Enc_Only':
model = get_model(args).Model(in_dim=2, hidden_dim=32, out_dim=1, num_layer=1).to(device)
model.apply(init_weights)
else:
model = get_model(args).Model(in_dim=2, hidden_dim=512, out_dim=1, num_layer=4).to(device)
model.apply(init_weights)
optim = LBFGS(model.parameters(), line_search_fn='strong_wolfe')
print(model)
print(get_n_params(model))
loss_track = []
# for region optimization
initial_region = args.initial_region
sample_num = args.sample_num
past_iterations = args.past_iterations
gradient_list_overall = []
gradient_list_temp = []
gradient_variance = 1
for i in tqdm(range(1000)):
###### Region Optimization with Monte Carlo Approximation ######
def closure():
x_res_region_sample_list = []
t_res_region_sample_list = []
for i in range(sample_num):
x_region_sample = (torch.rand(x_res.shape).to(x_res.device)) * np.clip(initial_region / gradient_variance,
a_min=0,
a_max=0.01)
t_region_sample = (torch.rand(x_res.shape).to(t_res.device)) * np.clip(initial_region / gradient_variance,
a_min=0,
a_max=0.01)
x_res_region_sample_list.append(x_res + x_region_sample)
t_res_region_sample_list.append(t_res + t_region_sample)
x_res_region_sample = torch.cat(x_res_region_sample_list, dim=0)
t_res_region_sample = torch.cat(t_res_region_sample_list, dim=0)
pred_res = model(x_res_region_sample, t_res_region_sample)
pred_left = model(x_left, t_left)
pred_right = model(x_right, t_right)
pred_upper = model(x_upper, t_upper)
pred_lower = model(x_lower, t_lower)
u_x = \
torch.autograd.grad(pred_res, x_res_region_sample, grad_outputs=torch.ones_like(pred_res),
retain_graph=True,
create_graph=True)[0]
u_t = \
torch.autograd.grad(pred_res, t_res_region_sample, grad_outputs=torch.ones_like(pred_res),
retain_graph=True,
create_graph=True)[0]
loss_res = torch.mean((u_t - 5 * pred_res * (1 - pred_res)) ** 2)
loss_bc = torch.mean((pred_upper - pred_lower) ** 2)
loss_ic = torch.mean(
(pred_left[:, 0] - torch.exp(- (x_left[:, 0] - torch.pi) ** 2 / (2 * (torch.pi / 4) ** 2))) ** 2)
loss_track.append([loss_res.item(), loss_bc.item(), loss_ic.item()])
loss = loss_res + loss_bc + loss_ic
optim.zero_grad()
loss.backward(retain_graph=True)
gradient_list_temp.append(torch.cat([(p.grad.view(-1)) if p.grad is not None else torch.zeros(1).cuda() for p in
model.parameters()]).cpu().numpy()) # hook gradients from computation graph
return loss
optim.step(closure)
###### Trust Region Calibration ######
gradient_list_overall.append(np.mean(np.array(gradient_list_temp), axis=0))
gradient_list_overall = gradient_list_overall[-past_iterations:]
gradient_list = np.array(gradient_list_overall)
gradient_variance = (
np.std(gradient_list, axis=0) / (np.mean(np.abs(gradient_list), axis=0) + 1e-6)).mean()
gradient_list_temp = []
if gradient_variance == 0:
gradient_variance = 1 # for numerical stability
print('Loss Res: {:4f}, Loss_BC: {:4f}, Loss_IC: {:4f}'.format(loss_track[-1][0], loss_track[-1][1], loss_track[-1][2]))
print('Train Loss: {:4f}'.format(np.sum(loss_track[-1])))
if not os.path.exists('./results/'):
os.makedirs('./results/')
torch.save(model.state_dict(), f'./results/1dreaction_{args.model}_region.pt')
# Visualize
if args.model == 'PINNsFormer' or args.model == 'PINNsFormer_Enc_Only':
res_test = make_time_sequence(res_test, num_step=5, step=1e-4)
res_test = torch.tensor(res_test, dtype=torch.float32, requires_grad=True).to(device)
x_test, t_test = res_test[:, ..., 0:1], res_test[:, ..., 1:2]
with torch.no_grad():
pred = model(x_test, t_test)[:, 0:1]
pred = pred.cpu().detach().numpy()
pred = pred.reshape(101, 101)
def h(x):
return np.exp(- (x - np.pi) ** 2 / (2 * (np.pi / 4) ** 2))
def u_ana(x, t):
return h(x) * np.exp(5 * t) / (h(x) * np.exp(5 * t) + 1 - h(x))
res_test, _, _, _, _ = get_data([0, 2 * np.pi], [0, 1], 101, 101)
u = u_ana(res_test[:, 0], res_test[:, 1]).reshape(101, 101)
rl1 = np.sum(np.abs(u - pred)) / np.sum(np.abs(u))
rl2 = np.sqrt(np.sum((u - pred) ** 2) / np.sum(u ** 2))
print('relative L1 error: {:4f}'.format(rl1))
print('relative L2 error: {:4f}'.format(rl2))
plt.figure(figsize=(4, 3))
plt.imshow(pred, aspect='equal')
plt.xlabel('x')
plt.ylabel('t')
plt.title('Predicted u(x,t)')
plt.colorbar()
plt.tight_layout()
plt.axis('off')
plt.savefig(f'./results/1dreaction_{args.model}_region_optimization_pred.pdf', bbox_inches='tight')
plt.figure(figsize=(4, 3))
plt.imshow(u, aspect='equal')
plt.xlabel('x')
plt.ylabel('t')
plt.title('Exact u(x,t)')
plt.colorbar()
plt.tight_layout()
plt.axis('off')
plt.savefig('./results/1dreaction_exact.pdf', bbox_inches='tight')
plt.figure(figsize=(4, 3))
plt.imshow(pred - u, aspect='equal', cmap='coolwarm', vmin=-0.15, vmax=0.15)
plt.xlabel('x')
plt.ylabel('t')
plt.title('Absolute Error')
plt.colorbar()
plt.tight_layout()
plt.axis('off')
plt.savefig(f'./results/1dreaction_{args.model}_region_optimization_error.pdf', bbox_inches='tight')