Note
Go to the end to download the full example code
Burgers dataset¶
Dataset consisting of solutions to Burgers’ equation.
from __future__ import annotations
from gemseo import configure_logger
from gemseo import create_benchmark_dataset
from gemseo.post.dataset.curves import Curves
configure_logger()
<RootLogger root (INFO)>
Load Burgers’ dataset¶
We can easily load this dataset
by means of the high-level function create_benchmark_dataset():
dataset = create_benchmark_dataset("BurgersDataset")
print(dataset)
GROUP inputs outputs ...
VARIABLE t u_t ...
COMPONENT 0 0 1 ... 498 499 500
0 0.000000 -8.610583e-43 0.012566 ... -0.025133 -0.012566 8.610583e-43
1 0.068966 -2.580645e-01 -0.246309 ... -0.281576 -0.269820 -2.580645e-01
2 0.137931 -4.848485e-01 -0.473805 ... -0.506935 -0.495892 -4.848485e-01
3 0.206897 -6.857143e-01 -0.675302 ... -0.706539 -0.696126 -6.857143e-01
4 0.275862 -8.648649e-01 -0.855016 ... -0.884563 -0.874714 -8.648649e-01
5 0.344828 -1.025641e+00 -1.016297 ... -1.044329 -1.034985 -1.025641e+00
6 0.413793 -1.170732e+00 -1.161843 ... -1.188509 -1.179620 -1.170732e+00
7 0.482759 -1.302326e+00 -1.293851 ... -1.319276 -1.310801 -1.302326e+00
8 0.551724 -1.422222e+00 -1.414124 ... -1.438419 -1.430321 -1.422222e+00
9 0.620690 -1.531915e+00 -1.524161 ... -1.547404 -1.539655 -1.531904e+00
10 0.689655 -1.632653e+00 -1.625216 ... -1.642738 -1.636298 -1.629650e+00
11 0.758621 -1.725490e+00 -1.718345 ... -1.068848 -1.175574 -1.266034e+00
12 0.827586 -1.811321e+00 -1.804445 ... 1.494420 1.473941 1.447486e+00
13 0.896552 -1.890909e+00 -1.884283 ... 1.407409 1.413715 1.419947e+00
14 0.965517 -1.964912e+00 -1.958519 ... 1.218988 1.225377 1.231764e+00
15 1.034483 -2.033898e+00 -2.027722 ... 1.042093 1.048270 1.054446e+00
16 1.103448 -2.098361e+00 -2.092386 ... 0.876779 0.882753 8.887274e-01
17 1.172414 -2.158730e+00 -2.152946 ... 0.721961 0.727745 7.335297e-01
18 1.241379 -2.215385e+00 -2.209778 ... 0.576670 0.582276 5.878827e-01
19 1.310345 -2.268657e+00 -2.263218 ... 0.440053 0.445492 4.509310e-01
20 1.379310 -2.318841e+00 -2.313559 ... 0.311355 0.316637 3.219185e-01
21 1.448276 -2.366197e+00 -2.361064 ... 0.189909 0.195042 2.001743e-01
22 1.517241 -2.410959e+00 -2.405967 ... 0.075117 0.080109 8.510101e-02
23 1.586207 -2.453333e+00 -2.448474 ... -0.033553 -0.028694 -2.383501e-02
24 1.655172 -2.493506e+00 -2.488774 ... -0.136578 -0.131845 -1.271120e-01
25 1.724138 -2.531646e+00 -2.527033 ... -0.234386 -0.229773 -2.251598e-01
26 1.793103 -2.567901e+00 -2.563402 ... -0.327364 -0.322865 -3.183658e-01
27 1.862069 -2.602410e+00 -2.598019 ... -0.415861 -0.411470 -4.070798e-01
28 1.931034 -2.635294e+00 -2.631007 ... -0.500194 -0.495906 -4.916191e-01
29 2.000000 -2.666667e+00 -2.662478 ... -0.580649 -0.576460 -5.722716e-01
[30 rows x 502 columns]
Show the input and output data¶
print(dataset.input_dataset)
print(dataset.output_dataset)
GROUP inputs
VARIABLE t
COMPONENT 0
0 0.000000
1 0.068966
2 0.137931
3 0.206897
4 0.275862
5 0.344828
6 0.413793
7 0.482759
8 0.551724
9 0.620690
10 0.689655
11 0.758621
12 0.827586
13 0.896552
14 0.965517
15 1.034483
16 1.103448
17 1.172414
18 1.241379
19 1.310345
20 1.379310
21 1.448276
22 1.517241
23 1.586207
24 1.655172
25 1.724138
26 1.793103
27 1.862069
28 1.931034
29 2.000000
GROUP outputs ...
VARIABLE u_t ...
COMPONENT 0 1 2 ... 498 499 500
0 -8.610583e-43 0.012566 0.025133 ... -0.025133 -0.012566 8.610583e-43
1 -2.580645e-01 -0.246309 -0.234553 ... -0.281576 -0.269820 -2.580645e-01
2 -4.848485e-01 -0.473805 -0.462762 ... -0.506935 -0.495892 -4.848485e-01
3 -6.857143e-01 -0.675302 -0.664890 ... -0.706539 -0.696126 -6.857143e-01
4 -8.648649e-01 -0.855016 -0.845166 ... -0.884563 -0.874714 -8.648649e-01
5 -1.025641e+00 -1.016297 -1.006953 ... -1.044329 -1.034985 -1.025641e+00
6 -1.170732e+00 -1.161843 -1.152955 ... -1.188509 -1.179620 -1.170732e+00
7 -1.302326e+00 -1.293851 -1.285376 ... -1.319276 -1.310801 -1.302326e+00
8 -1.422222e+00 -1.414124 -1.406026 ... -1.438419 -1.430321 -1.422222e+00
9 -1.531915e+00 -1.524161 -1.516407 ... -1.547404 -1.539655 -1.531904e+00
10 -1.632653e+00 -1.625216 -1.617779 ... -1.642738 -1.636298 -1.629650e+00
11 -1.725490e+00 -1.718345 -1.711199 ... -1.068848 -1.175574 -1.266034e+00
12 -1.811321e+00 -1.804445 -1.797569 ... 1.494420 1.473941 1.447486e+00
13 -1.890909e+00 -1.884283 -1.877657 ... 1.407409 1.413715 1.419947e+00
14 -1.964912e+00 -1.958519 -1.952125 ... 1.218988 1.225377 1.231764e+00
15 -2.033898e+00 -2.027722 -2.021545 ... 1.042093 1.048270 1.054446e+00
16 -2.098361e+00 -2.092386 -2.086412 ... 0.876779 0.882753 8.887274e-01
17 -2.158730e+00 -2.152946 -2.147161 ... 0.721961 0.727745 7.335297e-01
18 -2.215385e+00 -2.209778 -2.204172 ... 0.576670 0.582276 5.878827e-01
19 -2.268657e+00 -2.263218 -2.257778 ... 0.440053 0.445492 4.509310e-01
20 -2.318841e+00 -2.313559 -2.308278 ... 0.311355 0.316637 3.219185e-01
21 -2.366197e+00 -2.361064 -2.355932 ... 0.189909 0.195042 2.001743e-01
22 -2.410959e+00 -2.405967 -2.400975 ... 0.075117 0.080109 8.510101e-02
23 -2.453333e+00 -2.448474 -2.443615 ... -0.033553 -0.028694 -2.383501e-02
24 -2.493506e+00 -2.488774 -2.484041 ... -0.136578 -0.131845 -1.271120e-01
25 -2.531646e+00 -2.527033 -2.522420 ... -0.234386 -0.229773 -2.251598e-01
26 -2.567901e+00 -2.563402 -2.558903 ... -0.327364 -0.322865 -3.183658e-01
27 -2.602410e+00 -2.598019 -2.593628 ... -0.415861 -0.411470 -4.070798e-01
28 -2.635294e+00 -2.631007 -2.626719 ... -0.500194 -0.495906 -4.916191e-01
29 -2.666667e+00 -2.662478 -2.658289 ... -0.580649 -0.576460 -5.722716e-01
[30 rows x 501 columns]
Load customized dataset¶
Load the data with custom parameters and input-output naming.
dataset = create_benchmark_dataset(
"BurgersDataset", n_samples=20, n_x=700, fluid_viscosity=0.03
)
print(dataset)
GROUP inputs outputs ...
VARIABLE t u_t ...
COMPONENT 0 0 1 ... 697 698 699
0 0.000000 -8.337238e-143 0.008989 ... -0.017978 -0.008989 8.337238e-143
1 0.105263 -3.809524e-01 -0.372820 ... -0.397218 -0.389085 -3.809524e-01
2 0.210526 -6.956522e-01 -0.688227 ... -0.710503 -0.703078 -6.956522e-01
3 0.315789 -9.600000e-01 -0.953168 ... -0.973663 -0.966832 -9.600000e-01
4 0.421053 -1.185185e+00 -1.178860 ... -1.197836 -1.191511 -1.185185e+00
5 0.526316 -1.379310e+00 -1.373421 ... -1.391089 -1.385200 -1.379310e+00
6 0.631579 -1.548387e+00 -1.542878 ... -1.559406 -1.553896 -1.548387e+00
7 0.736842 -1.696970e+00 -1.691794 ... -1.707233 -1.702094 -1.696940e+00
8 0.842105 -1.828571e+00 -1.823692 ... 1.572538 1.577416 1.582292e+00
9 0.947368 -1.945946e+00 -1.941330 ... 1.271323 1.275939 1.280555e+00
10 1.052632 -2.051282e+00 -2.046903 ... 1.000999 1.005378 1.009757e+00
11 1.157895 -2.146341e+00 -2.142176 ... 0.757047 0.761213 7.653786e-01
12 1.263158 -2.232558e+00 -2.228586 ... 0.535789 0.539761 5.437330e-01
13 1.368421 -2.311111e+00 -2.307316 ... 0.334199 0.337994 3.417894e-01
14 1.473684 -2.382979e+00 -2.379345 ... 0.149765 0.153399 1.570324e-01
15 1.578947 -2.448980e+00 -2.445494 ... -0.019613 -0.016128 -1.264243e-02
16 1.684211 -2.509804e+00 -2.506455 ... -0.175707 -0.172358 -1.690094e-01
17 1.789474 -2.566038e+00 -2.562815 ... -0.320020 -0.316797 -3.135751e-01
18 1.894737 -2.618182e+00 -2.615077 ... -0.453837 -0.450732 -4.476269e-01
19 2.000000 -2.666667e+00 -2.663670 ... -0.578264 -0.575268 -5.722716e-01
[20 rows x 701 columns]
Plot the data¶
Curves(dataset, "x", "u_t").execute(save=False, show=True)
[<Figure size 640x480 with 1 Axes>]
Total running time of the script: ( 0 minutes 0.615 seconds)