1{
 2  "seed": 2085,
 3  "predictions": {
 4    "parseval_identity": {
 5      "predicted_relative_error": "machine precision",
 6      "observed": 3.387406547279367e-16
 7    },
 8    "exact_test_derivative": {
 9      "predicted_relative_error": "machine precision for resolved modes",
10      "observed": 1.8927561937532577e-14
11    },
12    "dealiasing": {
13      "prediction": "quadratic products are accurate in retained 2/3 band when kmax<=N/3; raw aliasing rises beyond it",
14      "observed": [
15        {
16          "kmax_over_N": 0.1,
17          "raw_rel_error_2/3": 4.195332171678912e-16,
18          "dealiased_rel_error_2/3": 3.819057284645697e-16
19        },
20        {
21          "kmax_over_N": 0.2,
22          "raw_rel_error_2/3": 3.160253883357437e-16,
23          "dealiased_rel_error_2/3": 4.95540206017975e-16
24        },
25        {
26          "kmax_over_N": 0.3,
27          "raw_rel_error_2/3": 2.841444531756777e-16,
28          "dealiased_rel_error_2/3": 4.0308764699249717e-16
29        },
30        {
31          "kmax_over_N": 0.333,
32          "raw_rel_error_2/3": 2.745074065857283e-16,
33          "dealiased_rel_error_2/3": 3.602436668598704e-16
34        },
35        {
36          "kmax_over_N": 0.4,
37          "raw_rel_error_2/3": 0.1000769595454345,
38          "dealiased_rel_error_2/3": 4.351676633801231e-16
39        },
40        {
41          "kmax_over_N": 0.45,
42          "raw_rel_error_2/3": 0.2050914414746415,
43          "dealiased_rel_error_2/3": 3.8910892004468816e-16
44        }
45      ]
46    },
47    "frequency_truncation": {
48      "prediction": "retained spectral energy equals Parseval physical projection energy",
49      "observed": [
50        {
51          "cutoff": 2,
52          "spectral_fraction": 3.2094490863833343e-32,
53          "physical_projection_fraction": 3.208610512269013e-32,
54          "abs_gap": 8.385741143213741e-36
55        },
56        {
57          "cutoff": 4,
58          "spectral_fraction": 0.7751937984496123,
59          "physical_projection_fraction": 0.7751937984496123,
60          "abs_gap": 0.0
61        },
62        {
63          "cutoff": 8,
64          "spectral_fraction": 0.7751937984496123,
65          "physical_projection_fraction": 0.7751937984496123,
66          "abs_gap": 0.0
67        },
68        {
69          "cutoff": 16,
70          "spectral_fraction": 0.9689922480620154,
71          "physical_projection_fraction": 0.9689922480620154,
72          "abs_gap": 0.0
73        },
74        {
75          "cutoff": 32,
76          "spectral_fraction": 1.0,
77          "physical_projection_fraction": 1.0000000000000002,
78          "abs_gap": 2.220446049250313e-16
79        },
80        {
81          "cutoff": 64,
82          "spectral_fraction": 1.0,
83          "physical_projection_fraction": 1.0,
84          "abs_gap": 0.0
85        }
86      ]
87    }
88  },
89  "speed_benchmark": {
90    "fft_ms": 0.3069089667405933,
91    "direct_ms": 19.459509932979323,
92    "direct_over_fft": 63.40482697407455,
93    "projection_rel_check": 6.969576594579571e-15
94  },
95  "burgers_mini_experiment": {
96    "error": "RuntimeError: One of the differentiated Tensors does not require grad"
97  }
98}