{
  "seed": 2085,
  "predictions": {
    "parseval_identity": {
      "predicted_relative_error": "machine precision",
      "observed": 3.387406547279367e-16
    },
    "exact_test_derivative": {
      "predicted_relative_error": "machine precision for resolved modes",
      "observed": 1.8927561937532577e-14
    },
    "dealiasing": {
      "prediction": "quadratic products are accurate in retained 2/3 band when kmax<=N/3; raw aliasing rises beyond it",
      "observed": [
        {
          "kmax_over_N": 0.1,
          "raw_rel_error_2/3": 4.195332171678912e-16,
          "dealiased_rel_error_2/3": 3.819057284645697e-16
        },
        {
          "kmax_over_N": 0.2,
          "raw_rel_error_2/3": 3.160253883357437e-16,
          "dealiased_rel_error_2/3": 4.95540206017975e-16
        },
        {
          "kmax_over_N": 0.3,
          "raw_rel_error_2/3": 2.841444531756777e-16,
          "dealiased_rel_error_2/3": 4.0308764699249717e-16
        },
        {
          "kmax_over_N": 0.333,
          "raw_rel_error_2/3": 2.745074065857283e-16,
          "dealiased_rel_error_2/3": 3.602436668598704e-16
        },
        {
          "kmax_over_N": 0.4,
          "raw_rel_error_2/3": 0.1000769595454345,
          "dealiased_rel_error_2/3": 4.351676633801231e-16
        },
        {
          "kmax_over_N": 0.45,
          "raw_rel_error_2/3": 0.2050914414746415,
          "dealiased_rel_error_2/3": 3.8910892004468816e-16
        }
      ]
    },
    "frequency_truncation": {
      "prediction": "retained spectral energy equals Parseval physical projection energy",
      "observed": [
        {
          "cutoff": 2,
          "spectral_fraction": 3.2094490863833343e-32,
          "physical_projection_fraction": 3.208610512269013e-32,
          "abs_gap": 8.385741143213741e-36
        },
        {
          "cutoff": 4,
          "spectral_fraction": 0.7751937984496123,
          "physical_projection_fraction": 0.7751937984496123,
          "abs_gap": 0.0
        },
        {
          "cutoff": 8,
          "spectral_fraction": 0.7751937984496123,
          "physical_projection_fraction": 0.7751937984496123,
          "abs_gap": 0.0
        },
        {
          "cutoff": 16,
          "spectral_fraction": 0.9689922480620154,
          "physical_projection_fraction": 0.9689922480620154,
          "abs_gap": 0.0
        },
        {
          "cutoff": 32,
          "spectral_fraction": 1.0,
          "physical_projection_fraction": 1.0000000000000002,
          "abs_gap": 2.220446049250313e-16
        },
        {
          "cutoff": 64,
          "spectral_fraction": 1.0,
          "physical_projection_fraction": 1.0,
          "abs_gap": 0.0
        }
      ]
    }
  },
  "speed_benchmark": {
    "fft_ms": 0.3069089667405933,
    "direct_ms": 19.459509932979323,
    "direct_over_fft": 63.40482697407455,
    "projection_rel_check": 6.969576594579571e-15
  },
  "burgers_mini_experiment": {
    "error": "RuntimeError: One of the differentiated Tensors does not require grad"
  }
}