-
Notifications
You must be signed in to change notification settings - Fork 0
/
Pendulum_Confidence_Plot_Fig_2.py
321 lines (286 loc) · 15 KB
/
Pendulum_Confidence_Plot_Fig_2.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
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
# # Script for the system identification of a non_linear pendulum using REN-ODEs.
###################################################################################
# from examples.train_pendulum import generate_train_test_pendulum,generate_pendulum_dataset
from examples.train_pendulum import generate_pendulum_dataset
from examples.train_pendulum import generate_uniform_test_pendulum
from models.NODE_REN import NODE_REN
from datalog.datalog import makedirs
import torch
from torch import nn
import matplotlib.pyplot as plt
import matplotlib
import numpy as np
import time
from math import pi as pi
from torchdiffeq import odeint_adjoint as odeint
import os
import glob
import argparse
def count_parameters(model):
return sum(p.numel() for p in model.parameters() if p.requires_grad)
class NFE_average():
"ARX to calculate the average of the number of function evaluations (NFEs)"
def __init__(self, mu=0.85):
self.average = None
self.mu = mu
def update(self, value):
if (self.average == None):
self.average = value
else:
self.average = self.mu * value + (1-self.mu)*self.average
self.average = np.round(self.average)
if __name__ == '__main__':
parser = argparse.ArgumentParser()
parser.add_argument('--nx', type=int, default=4,
help="No. of states of the model.")
parser.add_argument('--nq', type=int, default=5,
help="No. of nonlinear feedbacks.")
parser.add_argument('--n_steps', type=int, default=400,
help="No. of steps used during simulations.")
parser.add_argument('--t_end', type=float, default=8.,
help="Dimension of the time window [0, t_end].")
parser.add_argument('--sigma', type=str, default='tanh',
help="Activation function of NODE_REN.")
parser.add_argument('--method', type=str, default='rk4',
help="Integration method.")
parser.add_argument('--seed', type=int, default=10,
help="No. of the seed used during simulation.")
parser.add_argument('--epochs', type=int, default=30,
help="(Max) no. of epochs to be used.")
parser.add_argument('--batch_size', type=int,
default=20, help="Size of the batches.")
parser.add_argument('--alpha', type=float, default=0.0,
help="Contractivity rate.")
parser.add_argument('--device', type=str, default='cpu',
help="Choice of the computational device ('cpu' or 'cuda').")
parser.add_argument('--n_cuda', type=int, default=3,
help="Choice of the Cuda device.")
parser.add_argument('--learning_rate', type=float,
default=10.e-3, help="Learning rate.")
parser.add_argument('--n_exp', type=int, default=400,
help="No. of initial (random) states of the robots to consider for training AND testing.")
parser.add_argument('--verbose', type=str, default='p',
help="Sets the verbosity level. -'n': none; -'e': once per epoch; -'p': once per iteration; -'g': partial + gradient evaluation (heavy).")
parser.add_argument('--rtol', type=float, default=1.e-7,
help="relative tolerance for 'dopri5'")
parser.add_argument('--atol', type=float, default=1.e-9,
help="absolute tolerance for 'dopri5'")
parser.add_argument('--steps_integration', type=int, default=110,
help="Number of integration steps used in fixed-steps methods.")
parser.add_argument('--n_experiment', type=int, default=0)
parser.add_argument('--t_stop_training', type=float, default=3.0,
help="Stop time of the simulation during training.")
args = parser.parse_args()
if (args.device.lower() == 'cuda'):
device = torch.device('cuda:'+str(args.n_cuda)
if torch.cuda.is_available() else 'cpu')
else:
device = torch.device('cpu')
seed = args.seed
torch.manual_seed(seed)
# verbose = 'n' # none
# verbose = 'e' # only epoch
# verbose = 'p' # partial
# verbose = 'g' #partial + gradient evaluation. (heavy)
verbose = args.verbose.lower()
if not (verbose == 'n' or verbose == 'e' or verbose == 'p' or verbose == 'g'):
print("Set wrong value of verbose. The available ones are 'n', 'e', 'p' and 'g'. ")
print("Verbose was set to 'p'.")
verbose = 'p'
# # S I M U L A T I O N P H A S E
# # --------------------------------------------------------------------------------------------------------------------------------------------
# # Select network parameters
n_steps = args.n_steps
t_i = 0.0
t_end = args.t_end
n_time_vectors = 1
time_vectors = (t_end-t_i)*torch.rand(int(n_steps)-2, n_time_vectors,
device=device)+t_i*torch.ones(int(n_steps)-2, n_time_vectors, device=device)
time_vectors = torch.cat((t_i*torch.ones(1, n_time_vectors, device=device),
time_vectors, t_end*torch.ones(1, n_time_vectors, device=device)))
time_vectors, _ = torch.sort(time_vectors, 0)
time_vectors = torch.unique(time_vectors, dim=0)
time_vector = time_vectors[:, args.n_experiment]
real_beta = 1.5
real_l = 0.5
model_parameters = [real_beta, real_l]
n_exp = args.n_exp
destination_folder = f"./simulations/pendulum/Seed_{seed}/Comparison_GNODEREN__CNODEREN"
makedirs(destination_folder)
learning_rate = args.learning_rate
epochs = args.epochs
batch_size = args.batch_size
tol_loss = 1.0e-4
steps_integration = args.steps_integration
h = float((t_end - t_i)/(steps_integration-1))
out = generate_pendulum_dataset(n_exp=n_exp,
model_parameters=model_parameters,
time_vector=time_vector,
n_steps=n_steps,
seed=seed,
batch_size=batch_size,
device=device)
# # TOTAL_DATASETS = [n_steps(time) , n_experiments, nx==2]
my_z0s, my_outputs, domain, training_generator, partition = out
std_noise = 0.05
additive_noise = std_noise*torch.randn(my_outputs.shape, device=device)
my_outputs = my_outputs + std_noise * \
torch.randn(my_outputs.shape, device=device)
my_z0s = my_outputs[0, :, :]
training_size = len(partition['train'])
testing_size = len(partition['test'])
# # T R A I N I N G P H A S E
# # -------------------------------------------------------------------------------------------------------------------------------------------
# # Select hyper-parameters of the model
nx = args.nx
nq = args.nq
ny = 2
nu = 1
sigma = args.sigma
alpha = args.alpha
epsilon = 5.0e-2
model_NODEREN = NODE_REN(nx, ny, nu, nq, sigma, epsilon,
mode="c", device=device, alpha=alpha).to(device)
model_G_NODEREN = NODE_REN(
nx, ny, nu, nq, sigma, epsilon, mode="general", device=device).to(device)
NODEREN_folder = f"./simulations/pendulum/Seed_{seed}/{args.method}_{args.steps_integration}_{args.n_experiment}"
G_NODEREN_folder = f"./simulations/pendulum/Seed_{seed}/GNODEREN_{args.n_experiment}"
path_NODEREN = glob.glob(os.path.join(NODEREN_folder, '*.pt'))[0]
model_NODEREN.load_state_dict(torch.load(path_NODEREN, map_location='cpu'))
model_NODEREN.updateParameters()
path_G_NODEREN = glob.glob(os.path.join(G_NODEREN_folder, '*.pt'))[0]
model_G_NODEREN.load_state_dict(
torch.load(path_G_NODEREN, map_location='cpu'))
# method = args.method
MSE = nn.MSELoss()
loss_vector = np.zeros((1+epochs)*round(n_exp/batch_size))
start = time.time()
average_NFE_value = NFE_average()
t_stop = args.t_stop_training
n_index_training = int(t_stop/t_end*n_steps)
time_vector_training = time_vector[0:n_index_training]
print("Starting Testing Phase")
with torch.no_grad():
method_testing = 'dopri5'
z_testing = my_outputs[:, partition['test'], :]
x0_testing = torch.zeros(testing_size, nx, device=device)
x0_testing[:, 0:2] = z_testing[0, :, :]
x_testing_NODEREN = odeint(
model_NODEREN, x0_testing, time_vector, method=method_testing)
y_testing_NODEREN = torch.empty(
n_steps, testing_size, ny, device=device)
for nt in range(n_steps):
y_testing_NODEREN[nt, :, :] = model_NODEREN.output(
time_vector[nt], x_testing_NODEREN[nt, :, :])
loss_testing_NODEREN = MSE(y_testing_NODEREN, z_testing)
x_testing_G_NODEREN = odeint(
model_G_NODEREN, x0_testing, time_vector, method=method_testing)
y_testing_G_NODEREN = torch.empty(
n_steps, testing_size, ny, device=device)
for nt in range(n_steps):
y_testing_G_NODEREN[nt, :, :] = model_G_NODEREN.output(
time_vector[nt], x_testing_G_NODEREN[nt, :, :])
loss_testing_G_NODEREN = MSE(y_testing_G_NODEREN, z_testing)
plt.rcParams['font.size'] = 15
for ind in range(3):
# plt.figure()
plt.figure("figsize", (6, 4))
plt.ylim((-2, 2))
plt.xlim((0, t_end))
plt.grid()
plt.plot(t_stop*np.array([1.0, 1.0]), 5.0 *
np.array([-1.0, 1.0]), 'k--', linewidth=1.5)
plt.plot(time_vector.cpu().detach().numpy(), z_testing[:, ind, 0].cpu(
).detach().numpy(), color='gray', linewidth=2.0, label='Target')
plt.plot(time_vector.cpu().detach().numpy(), y_testing_NODEREN[:, ind, 0].cpu(
).detach().numpy(), '--', color='orange', linewidth=2.5, label='NodeREN')
plt.plot(time_vector.cpu().detach().numpy(), y_testing_G_NODEREN[:, ind, 0].cpu(
).detach().numpy(), '--', color='tab:blue', linewidth=2.5, label='G-NodeREN')
plt.xlabel('Time [s]')
plt.ylabel(r'$\alpha$ [rad]')
plt.legend(loc='best')
file = os.path.join(destination_folder, f"Plot#{ind}_x1.pdf")
plt.savefig(file, bbox_inches='tight')
plt.figure()
plt.plot(time_vector.cpu().detach().numpy(), z_testing[:, ind, 1].cpu(
).detach().numpy(), linewidth=2.0, label='Target')
plt.plot(time_vector.cpu().detach().numpy(), y_testing_NODEREN[:, ind, 1].cpu(
).detach().numpy(), '--', linewidth=2.5, label='NodeREN')
plt.plot(time_vector.cpu().detach().numpy(), y_testing_G_NODEREN[:, ind, 1].cpu(
).detach().numpy(), '--', linewidth=2.5, label='G-NodeREN')
plt.xlabel('Time [s]')
plt.legend(loc='best')
plt.ylabel(r'$\alpha(t)$ [rad]')
file = os.path.join(destination_folder, f"Plot#{ind}_x2.pdf")
plt.savefig(file, bbox_inches='tight')
plt.close('all')
# # P L O T T I N G C O N F I D E N C E I N T E R V A L S
# # ---------------------------------------------------------------------------------------------------------------
print("Starting Confidence Regions Plots")
n_traj = 300
z_testing_confidence, _ = generate_uniform_test_pendulum(my_z0s[partition['test'], :].cpu(
).detach().numpy(), model_parameters, 0.0, t_end=t_end, n_steps=n_steps, seed=seed, device=device)
z_testing_confidence = z_testing_confidence + \
additive_noise[:, partition['test'], :]
# z_testing = z_testing + torch.randn(z_testing.shape,device =device)*std_noise
time_vector = torch.linspace(t_i, t_end, n_steps)
for k in range(6, 8):
method = 'dopri5'
with torch.no_grad():
z_plot = z_testing_confidence[:, k:k+1, :]
x0_plot = torch.zeros(n_traj, nx, device=device)
x0_plot[0, 0:2] = z_plot[0, 0, :]
for i in range(1, n_traj):
x0_plot[i, 0:2] = z_plot[0, 0, :] + torch.randn(2,)*0.1
# ,options={'step_size': h})
x_plot_NODEREN = odeint(
model_NODEREN, x0_plot, time_vector, method=method)
y_plot_NODEREN = torch.empty(
int(n_steps), n_traj, ny, device=device)
for nt in range(int(n_steps)):
y_plot_NODEREN[nt, :, :] = model_NODEREN.output(
time_vector[nt], x_plot_NODEREN[nt, :, :])
# ,options={'step_size': h})
x_plot_G_NODEREN = odeint(
model_G_NODEREN, x0_plot, time_vector, method=method)
y_plot_G_NODEREN = torch.empty(
int(n_steps), n_traj, ny, device=device)
for nt in range(int(n_steps)):
y_plot_G_NODEREN[nt, :, :] = model_G_NODEREN.output(
time_vector[nt], x_plot_G_NODEREN[nt, :, :])
confidence_interval1 = 95
confidence_interval2 = 80
confidence_interval3 = 50
# plt.figure()
plt.figure("figsize", (6, 4))
matplotlib.rcParams['text.usetex'] = True
plt.grid(alpha=0.8)
for ci in [confidence_interval1, confidence_interval2, confidence_interval3]:
low_NODEREN = np.percentile(y_plot_NODEREN[:, :, 0].transpose(
1, 0).cpu().detach().numpy(), 50 - ci / 2, axis=0)
high_NODEREN = np.percentile(y_plot_NODEREN[:, :, 0].transpose(
1, 0).cpu().detach().numpy(), 50 + ci / 2, axis=0)
plt.fill_between(time_vector.cpu().detach().numpy(
), low_NODEREN, high_NODEREN, color='orange', alpha=0.2)
low_G_NODEREN = np.percentile(y_plot_G_NODEREN[:, :, 0].transpose(
1, 0).cpu().detach().numpy(), 50 - ci / 2, axis=0)
high_G_NODEREN = np.percentile(y_plot_G_NODEREN[:, :, 0].transpose(
1, 0).cpu().detach().numpy(), 50 + ci / 2, axis=0)
plt.fill_between(time_vector.cpu().detach().numpy(
), low_G_NODEREN, high_G_NODEREN, color='tab:blue', alpha=0.18)
plt.plot(t_stop*np.array([1.0, 1.0]), 10.0 *
np.array([-1.0, 1.0]), 'k--', label='_nolegend_')
plt.plot(time_vector.cpu().detach().numpy(), z_plot[:, 0, 0].cpu().detach().numpy(), 'gray', linewidth=1.5,
label='Target')
plt.plot(time_vector.cpu().detach().numpy(), y_plot_NODEREN[:, 0, 0].cpu().detach().numpy(), "--", color='orange', linewidth=1,
label='C-NodeREN')
plt.plot(time_vector.cpu().detach().numpy(), y_plot_G_NODEREN[:, 0, 0].cpu().detach().numpy(), "--", color='tab:blue', linewidth=1,
label='G-NodeREN')
plt.xlabel('Time [s]')
plt.ylabel(r'${\alpha}(t)$ [rad]')
plt.legend(loc='best')
file = os.path.join(destination_folder, f"Plot_confidence_{k}_x1.pdf")
plt.ylim((-1, 2))
plt.xlim((0, 8.0))
plt.savefig(file, bbox_inches='tight')
plt.close('all')