{
  "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": 2.4595260620117188,
        "fd_ms": 1.1093616485595703,
        "speedup": 0.45104691740984876,
        "rmse": 8.095117763762474
      },
      {
        "N": 512,
        "nu": 0.001,
        "hopf_cole_ms": 0.06842613220214844,
        "fd_ms": 0.11301040649414062,
        "speedup": 1.651567944250871,
        "rmse": 1.561303593770873
      },
      {
        "N": 1024,
        "nu": 0.01,
        "hopf_cole_ms": 0.05984306335449219,
        "fd_ms": 4.583120346069336,
        "speedup": 76.58565737051792,
        "rmse": 19.902285633276207
      },
      {
        "N": 1024,
        "nu": 0.001,
        "hopf_cole_ms": 0.054836273193359375,
        "fd_ms": 0.4563331604003906,
        "speedup": 8.321739130434782,
        "rmse": 2.7342285097593564
      },
      {
        "N": 2048,
        "nu": 0.01,
        "hopf_cole_ms": 0.08845329284667969,
        "fd_ms": 19.593000411987305,
        "speedup": 221.5067385444744,
        "rmse": 39.14175495928565
      },
      {
        "N": 2048,
        "nu": 0.001,
        "hopf_cole_ms": 0.07510185241699219,
        "fd_ms": 1.9483566284179688,
        "speedup": 25.942857142857143,
        "rmse": 4.963314310186603
      }
    ],
    "fokas_vs_fourier": [
      {
        "method": "fokas",
        "N": 64,
        "rmse": 0.013722927804692983,
        "time_ms": 1.7440319061279297
      },
      {
        "method": "fokas",
        "N": 128,
        "rmse": 0.015599436271601716,
        "time_ms": 3.344297409057617
      },
      {
        "method": "fokas",
        "N": 256,
        "rmse": 0.016095097819050174,
        "time_ms": 6.840944290161133
      },
      {
        "method": "fokas",
        "N": 512,
        "rmse": 0.01621861137592211,
        "time_ms": 14.413833618164062
      },
      {
        "method": "fourier",
        "N": 50,
        "rmse": 0.25729521057061433,
        "time_ms": 2.101898193359375
      },
      {
        "method": "fourier",
        "N": 100,
        "rmse": 0.25729521057061433,
        "time_ms": 4.0283203125
      },
      {
        "method": "fourier",
        "N": 500,
        "rmse": 0.25729521057061433,
        "time_ms": 20.289897918701172
      },
      {
        "method": "fourier",
        "N": 1000,
        "rmse": 0.25729521057061433,
        "time_ms": 40.23003578186035
      },
      {
        "method": "fourier",
        "N": 2000,
        "rmse": 0.25729521057061433,
        "time_ms": 80.52802085876465
      },
      {
        "method": "burgers_fokas",
        "time_ms": 7.393360137939453
      },
      {
        "method": "burgers_fft",
        "time_ms": 0.07486343383789062
      }
    ]
  }
}