/
easyvvuq_fusion_tutorial.py
executable file
·222 lines (188 loc) · 9.15 KB
/
easyvvuq_fusion_tutorial.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
#! /usr/bin/env python
"""
Run an EasyVVUQ campaign to analyze the sensitivity of the temperature
profile predicted by a simplified model of heat conduction in a
tokamak plasma.
This is done with PCE.
"""
import os
import easyvvuq as uq
import chaospy as cp
import pickle
import time
import numpy as np
import matplotlib.pylab as plt
time_start = time.time()
# Set up a fresh campaign called "fusion_pce."
my_campaign = uq.Campaign(name='fusion_pce.')
# Define parameter space
params = {
"Qe_tot": {"type": "float", "min": 1.0e6, "max": 50.0e6, "default": 2e6},
"H0": {"type": "float", "min": 0.00, "max": 1.0, "default": 0},
"Hw": {"type": "float", "min": 0.01, "max": 100.0, "default": 0.1},
"Te_bc": {"type": "float", "min": 10.0, "max": 1000.0, "default": 100},
"chi": {"type": "float", "min": 0.01, "max": 100.0, "default": 1},
"a0": {"type": "float", "min": 0.2, "max": 10.0, "default": 1},
"R0": {"type": "float", "min": 0.5, "max": 20.0, "default": 3},
"E0": {"type": "float", "min": 1.0, "max": 10.0, "default": 1.5},
"b_pos": {"type": "float", "min": 0.95, "max": 0.99, "default": 0.98},
"b_height": {"type": "float", "min": 3e19, "max": 10e19, "default": 6e19},
"b_sol": {"type": "float", "min": 2e18, "max": 3e19, "default": 2e19},
"b_width": {"type": "float", "min": 0.005, "max": 0.025, "default": 0.01},
"b_slope": {"type": "float", "min": 0.0, "max": 0.05, "default": 0.01},
"nr": {"type": "integer", "min": 10, "max": 1000, "default": 100},
"dt": {"type": "float", "min": 1e-3, "max": 1e3, "default": 100},
"out_file": {"type": "string", "default": "output.csv"}
}
""" code snippet for writing the template file
str = ""
first = True
for k in params.keys():
if first:
str += '{"%s": "$%s"' % (k,k) ; first = False
else:
str += ', "%s": "$%s"' % (k,k)
str += '}'
print(str, file=open('fusion.template','w'))
"""
# Create an encoder, decoder and collater for PCE test app
encoder = uq.encoders.GenericEncoder(template_fname='fusion.template',
delimiter='$',
target_filename='fusion_in.json')
decoder = uq.decoders.SimpleCSV(target_filename="output.csv",
output_columns=["te", "ne", "rho", "rho_norm"])
execute = uq.actions.ExecuteLocal('python3 %s/fusion_model.py fusion_in.json' % (os.getcwd()))
actions = uq.actions.Actions(uq.actions.CreateRunDirectory('/tmp'),
uq.actions.Encode(encoder), execute, uq.actions.Decode(decoder))
# Add the app (automatically set as current app)
my_campaign.add_app(name="fusion", params=params, actions=actions)
time_end = time.time()
print('Time for phase 1 = %.3f' % (time_end-time_start))
time_start = time.time()
# Create the sampler
vary = {
"Qe_tot": cp.Uniform(1.8e6, 2.2e6),
"H0": cp.Uniform(0.0, 0.2),
"Hw": cp.Uniform(0.1, 0.5),
"chi": cp.Uniform(0.8, 1.2),
"Te_bc": cp.Uniform(80.0, 120.0),
"b_pos": cp.Uniform(0.95, 0.99),
"b_height": cp.Uniform(5e19, 7e19),
"b_sol": cp.Uniform(1e19, 3e19),
"b_width": cp.Uniform(0.015, 0.025),
"b_slope": cp.Uniform(0.005, 0.020)
}
""" other possible quantities to vary
"a0": cp.Uniform(0.9, 1.1),
"R0": cp.Uniform(2.7, 3.3),
"E0": cp.Uniform(1.4, 1.6),
"b_pos": cp.Uniform(0.95, 0.99),
"b_height": cp.Uniform(5e19, 7e19),
"b_sol": cp.Uniform(1e19, 3e19),
"b_width": cp.Uniform(0.015, 0.025),
"b_slope": cp.Uniform(0.005, 0.020)
"""
# Associate a sampler with the campaign
my_campaign.set_sampler(uq.sampling.PCESampler(vary=vary, polynomial_order=1))
# Will draw all (of the finite set of samples)
my_campaign.draw_samples()
print('Number of samples = %s' % my_campaign.get_active_sampler().count)
time_end = time.time()
print('Time for phase 2 = %.3f' % (time_end-time_start))
time_start = time.time()
# Run and collate the cases
my_campaign.execute().collate()
results_df = my_campaign.get_collation_result()
time_end = time.time()
print('Time for phase 3 = %.3f' % (time_end-time_start))
time_start = time.time()
# Post-processing analysis
my_campaign.apply_analysis(uq.analysis.PCEAnalysis(sampler=my_campaign.get_active_sampler(), qoi_cols=["te", "ne", "rho", "rho_norm"]))
time_end = time.time()
print('Time for phase 4 = %.3f' % (time_end-time_start))
time_start = time.time()
# Get Descriptive Statistics
results = my_campaign.get_last_analysis()
rho = results.describe('rho', 'mean')
rho_norm = results.describe('rho_norm', 'mean')
time_end = time.time()
print('Time for phase 5 = %.3f' % (time_end-time_start))
time_start = time.time()
pickle.dump(results, open('fusion_results.pickle','bw'))
###saved_results = pickle.load(open('fusion_results.pickle','br'))
time_end = time.time()
print('Time for phase 6 = %.3f' % (time_end-time_start))
plt.ion()
# plot the calculated Te: mean, with std deviation, 10 and 90% and range
plt.figure()
plt.plot(rho, results.describe('te', 'mean'), 'b-', label='Mean')
plt.plot(rho, results.describe('te', 'mean')-results.describe('te', 'std'), 'b--', label='+1 std deviation')
plt.plot(rho, results.describe('te', 'mean')+results.describe('te', 'std'), 'b--')
plt.fill_between(rho, results.describe('te', 'mean')-results.describe('te', 'std'), results.describe('te', 'mean')+results.describe('te', 'std'), color='b', alpha=0.2)
plt.plot(rho, results.describe('te', '10%'), 'b:', label='10 and 90 percentiles')
plt.plot(rho, results.describe('te', '90%'), 'b:')
plt.fill_between(rho, results.describe('te', '10%'), results.describe('te', '90%'), color='b', alpha=0.1)
plt.fill_between(rho, results.describe('te', '1%'), results.describe('te', '99%'), color='b', alpha=0.05)
plt.legend(loc=0)
plt.xlabel('rho [m]')
plt.ylabel('Te [eV]')
plt.title(my_campaign.campaign_dir)
plt.savefig('Te.png')
# plot the first Sobol results
plt.figure()
for k in results.sobols_first()['te'].keys(): plt.plot(rho, results.sobols_first()['te'][k], label=k)
plt.legend(loc=0)
plt.xlabel('rho [m]')
plt.ylabel('sobols_first')
plt.title(my_campaign.campaign_dir)
plt.savefig('sobols_first.png')
# plot the second Sobol results
plt.figure()
for k1 in results.sobols_second()['te'].keys():
for k2 in results.sobols_second()['te'][k1].keys():
plt.plot(rho, results.sobols_second()['te'][k1][k2], label=k1+'/'+k2)
plt.legend(loc=0, ncol=2)
plt.xlabel('rho [m]')
plt.ylabel('sobols_second')
plt.title(my_campaign.campaign_dir+'\n');
plt.savefig('sobols_second.png')
# plot the total Sobol results
plt.figure()
for k in results.sobols_total()['te'].keys(): plt.plot(rho, results.sobols_total()['te'][k], label=k)
plt.legend(loc=0)
plt.xlabel('rho [m]')
plt.ylabel('sobols_total')
plt.title(my_campaign.campaign_dir)
plt.savefig('sobols_total.png')
### Commented out because we get "GaussianKDE()) has dangling dependencies" error messages
# # plot the distributions
# plt.figure()
# for i, D in enumerate(results.raw_data['output_distributions']['te']):
# _Te = np.linspace(D.lower[0], D.upper[0], 101)
# _DF = D.pdf(_Te)
# plt.loglog(_Te, _DF, 'b-', alpha=0.25)
# plt.loglog(results.describe('te', 'mean')[i], np.interp(results.describe('te', 'mean')[i], _Te, _DF), 'bo')
# plt.loglog(results.describe('te', 'mean')[i]-results.describe('te', 'std')[i], np.interp(results.describe('te', 'mean')[i]-results.describe('te', 'std')[i], _Te, _DF), 'b*')
# plt.loglog(results.describe('te', 'mean')[i]+results.describe('te', 'std')[i], np.interp(results.describe('te', 'mean')[i]+results.describe('te', 'std')[i], _Te, _DF), 'b*')
# plt.loglog(results.describe('te', '10%')[i], np.interp(results.describe('te', '10%')[i], _Te, _DF), 'b+')
# plt.loglog(results.describe('te', '90%')[i], np.interp(results.describe('te', '90%')[i], _Te, _DF), 'b+')
# plt.xlabel('Te')
# plt.ylabel('distribution function')
# plt.savefig('distribution_functions.png')
te_dist = results.raw_data['output_distributions']['te']
for i in [np.maximum(0, int(i-1)) for i in np.linspace(0,1,5) * rho_norm.shape]:
plt.figure()
pdf_raw_samples = cp.GaussianKDE(results_df.te[i])
pdf_kde_samples = cp.GaussianKDE(te_dist.samples[i])
plt.hist(results_df.te[i], density=True, bins=50, label='histogram of raw samples', alpha=0.25)
if hasattr(te_dist, 'samples'):
plt.hist(te_dist.samples[i], density=True, bins=50, label='histogram of kde samples', alpha=0.25)
plt.plot(np.linspace(pdf_raw_samples.lower, pdf_raw_samples.upper), pdf_raw_samples.pdf(np.linspace(pdf_raw_samples.lower, pdf_raw_samples.upper)), label='PDF (raw samples)')
plt.plot(np.linspace(pdf_kde_samples.lower, pdf_kde_samples.upper), pdf_kde_samples.pdf(np.linspace(pdf_kde_samples.lower, pdf_kde_samples.upper)), label='PDF (kde samples)')
if i==0:
t1 = te_dist[i]
plt.plot(np.linspace(t1.lower, t1.upper), t1.pdf(np.linspace(t1.lower,t1.upper)), label='PDF from EasyVVUQ')
plt.legend(loc=0)
plt.xlabel('Te [eV]')
plt.title('Distributions for rho_norm = %0.4f' % (rho_norm[i]))
plt.savefig('distribution_function_rho_norm=%0.4f.png' % (rho_norm[i]))