Unexpected discontinuity in Sobol' indices of heat PDE example
The differences between the Sobol' indices for the first input variable (initial temperature) between different time steps of the heat equation simulation are discontinuous when they should not be. The table below shows for every time step t
the p
-norm of (s(t+1) - s(t)) / s(t))
, where s(t)
is the vector of Sobol' indices at time t
and the division indicates the element-wise division of s(t+1) - s(t)
by s(t)
. Rows are highlighted if the maximum norm is larger than 100.
Time step | p=1 | p=2 | p=inf |
---|---|---|---|
0 | 102.62 | 9.27 | 1.28 |
1 | 3422.77 | 1614.63 | 1141.18 |
2 | 700.86 | 7.43 | 0.84 |
3 | 65.16 | 6.07 | 2.94 |
4 | 91.92 | 10.25 | 5.54 |
5 | 126.71 | 13.51 | 6.50 |
6 | 618.49 | 69.15 | 26.45 |
7 | 99.81 | 8.25 | 3.38 |
8 | 89.92 | 16.51 | 11.23 |
9 | 68.82 | 6.07 | 2.86 |
10 | 71.89 | 6.73 | 3.39 |
11 | 118.85 | 32.91 | 22.95 |
12 | 113.28 | 16.12 | 10.07 |
13 | 246.19 | 26.18 | 10.87 |
14 | 236.25 | 19.60 | 2.26 |
15 | 93.54 | 7.22 | 2.01 |
16 | 69.87 | 5.35 | 2.23 |
17 | 101.87 | 6.02 | 3.14 |
18 | 61.36 | 5.39 | 2.74 |
19 | 63.25 | 5.63 | 2.68 |
20 | 207.41 | 7.58 | 4.60 |
21 | 86.20 | 13.12 | 7.50 |
22 | 83.27 | 8.93 | 3.69 |
23 | 320.41 | 28.01 | 18.03 |
24 | 362.02 | 111.83 | 77.55 |
25 | 160.41 | 14.95 | 1.85 |
26 | 82.79 | 7.10 | 3.24 |
27 | 91.46 | 22.53 | 15.71 |
28 | 60.50 | 5.14 | 2.63 |
29 | 117.11 | 43.13 | 30.33 |
30 | 64.82 | 7.33 | 3.71 |
31 | 68.77 | 9.36 | 4.58 |
32 | 78.34 | 13.72 | 7.21 |
33 | 68.45 | 8.85 | 5.34 |
34 | 69.11 | 7.22 | 3.24 |
35 | 83.93 | 11.62 | 5.31 |
36 | 86.67 | 9.62 | 4.57 |
37 | 124.53 | 17.40 | 8.94 |
38 | 880.25 | 479.91 | 338.95 |
39 | 140.71 | 13.39 | 1.81 |
40 | 157.46 | 54.25 | 37.97 |
41 | 67.52 | 5.83 | 2.28 |
42 | 60.65 | 5.31 | 2.22 |
43 | 102.50 | 32.46 | 22.36 |
44 | 191.25 | 2.46 | 0.47 |
45 | 59.51 | 7.37 | 4.00 |
46 | 264.51 | 9.11 | 3.15 |
47 | 99.24 | 35.69 | 25.11 |
48 | 152.49 | 59.72 | 40.33 |
49 | 71.59 | 14.41 | 9.82 |
50 | 159.16 | 62.02 | 42.31 |
51 | 73.87 | 10.53 | 6.56 |
52 | 97.18 | 14.95 | 7.08 |
53 | 92.10 | 10.84 | 4.97 |
54 | 131.55 | 23.24 | 14.52 |
55 | 283.93 | 74.04 | 49.38 |
56 | 137.46 | 14.24 | 2.27 |
57 | 83.07 | 9.83 | 5.17 |
58 | 60.10 | 4.64 | 1.46 |
59 | 112.28 | 41.60 | 29.19 |
60 | 51.51 | 4.09 | 1.50 |
61 | 55.81 | 6.68 | 3.25 |
62 | 54.97 | 7.46 | 4.78 |
63 | 56.98 | 8.30 | 5.30 |
64 | 51.81 | 5.17 | 2.82 |
65 | 414.95 | 208.71 | 141.07 |
66 | 64.85 | 8.52 | 3.77 |
67 | 69.92 | 10.76 | 6.34 |
68 | 59.37 | 5.83 | 2.08 |
69 | 99.43 | 28.47 | 19.56 |
70 | 63.72 | 6.75 | 3.16 |
71 | 226.54 | 10.57 | 6.93 |
72 | 986.00 | 346.92 | 194.13 |
73 | 116.55 | 30.96 | 21.20 |
74 | 252.35 | 11.58 | 5.24 |
75 | 383.62 | 217.67 | 153.77 |
76 | 457.52 | 45.52 | 24.62 |
77 | 241.07 | 7.27 | 2.61 |
78 | 2504.18 | 541.77 | 209.76 |
79 | 55.88 | 5.51 | 2.77 |
80 | 52.92 | 4.76 | 2.12 |
81 | 75.55 | 15.15 | 7.54 |
82 | 128.14 | 50.50 | 35.21 |
83 | 84.81 | 22.46 | 14.83 |
84 | 56.49 | 6.55 | 2.51 |
85 | 52.06 | 5.02 | 1.69 |
86 | 68.96 | 13.69 | 8.34 |
87 | 66.41 | 12.32 | 7.56 |
88 | 54.46 | 6.23 | 3.25 |
89 | 56.82 | 6.84 | 3.42 |
90 | 1193.06 | 64.83 | 37.28 |
91 | 395.02 | 22.06 | 14.32 |
92 | 80.42 | 17.45 | 11.51 |
93 | 1548.98 | 156.57 | 106.85 |
94 | 113.39 | 44.76 | 31.49 |
95 | 745.03 | 486.78 | 344.17 |
96 | 852.48 | 39.83 | 20.21 |
97 | 84.18 | 11.17 | 4.30 |
98 | 186.10 | 74.18 | 52.10 |
Edited by Christoph Conrads