{
  "schema": "hopf_cole_benchmark_v2",
  "description": "Hopf-Cole solver benchmark with Fokas unified transform method",
  "reference": "arXiv:2605.11788 (Kalimeris, Mindrinos, Paraskevopoulos 2026)",
  "results": {
    "fft_vs_fd": [
      {
        "N": 512,
        "nu": 0.01,
        "hopf_cole_ms": 1.6825199127197266,
        "fd_ms": 1.3039112091064453,
        "speedup": 0.7749752019271645,
        "rmse": 8.095117763762474
      },
      {
        "N": 512,
        "nu": 0.001,
        "hopf_cole_ms": 0.09775161743164062,
        "fd_ms": 0.1285076141357422,
        "speedup": 1.3146341463414635,
        "rmse": 1.561303593770873
      },
      {
        "N": 1024,
        "nu": 0.01,
        "hopf_cole_ms": 0.06699562072753906,
        "fd_ms": 5.218505859375,
        "speedup": 77.8932384341637,
        "rmse": 19.902285633276207
      },
      {
        "N": 1024,
        "nu": 0.001,
        "hopf_cole_ms": 0.06937980651855469,
        "fd_ms": 0.5092620849609375,
        "speedup": 7.34020618556701,
        "rmse": 2.7342285097593564
      },
      {
        "N": 2048,
        "nu": 0.01,
        "hopf_cole_ms": 0.10156631469726562,
        "fd_ms": 21.08144760131836,
        "speedup": 207.56338028169014,
        "rmse": 39.14175495928565
      },
      {
        "N": 2048,
        "nu": 0.001,
        "hopf_cole_ms": 0.1201629638671875,
        "fd_ms": 1.916646957397461,
        "speedup": 15.950396825396826,
        "rmse": 4.963314310186603
      }
    ],
    "fokas_vs_fourier": [
      {
        "method": "fokas",
        "N": 64,
        "rmse": 0.013722927804692983,
        "time_ms": 2.4340152740478516
      },
      {
        "method": "fokas",
        "N": 128,
        "rmse": 0.015599436271601716,
        "time_ms": 4.050254821777344
      },
      {
        "method": "fokas",
        "N": 256,
        "rmse": 0.016095097819050174,
        "time_ms": 8.841991424560547
      },
      {
        "method": "fokas",
        "N": 512,
        "rmse": 0.01621861137592211,
        "time_ms": 22.000551223754883
      },
      {
        "method": "fourier",
        "N": 50,
        "rmse": 0.25729521057061433,
        "time_ms": 2.9892921447753906
      },
      {
        "method": "fourier",
        "N": 100,
        "rmse": 0.25729521057061433,
        "time_ms": 5.973100662231445
      },
      {
        "method": "fourier",
        "N": 500,
        "rmse": 0.25729521057061433,
        "time_ms": 26.767730712890625
      },
      {
        "method": "fourier",
        "N": 1000,
        "rmse": 0.25729521057061433,
        "time_ms": 51.476240158081055
      },
      {
        "method": "fourier",
        "N": 2000,
        "rmse": 0.25729521057061433,
        "time_ms": 96.56643867492676
      },
      {
        "method": "burgers_fokas",
        "time_ms": 8.424997329711914
      },
      {
        "method": "burgers_fft",
        "time_ms": 0.08177757263183594
      }
    ]
  }
}