mirror of
https://github.com/allaunthefox/Research-Stack.git
synced 2026-07-30 18:56:16 +00:00
4965029758
1. Singer Sidon Sets (2605.03274): - New SidonSets.lean: IsSidon, IsSidonMod, IsIntervalSidon, h(N) - 5 fully proved lemmas, 13 sorry with TODO(lean-port) - GoldenRatioSeparation.lean: singer_density_lt_golden (proved) - lake build: 3303 jobs, 0 errors 2. Hexagonal lattice + RG (2605.09974): - New test_hexagonal_lattice_rg() in unified_rg_tests.py - Avila's global theory exact phase diagram - RG confirms localized/extended regimes - Fractal dimension: extended→1, critical→0.5, localized→0 - 7 tests, all pass 3. Burgers + Hopf-Cole + Fokas (2605.11788): - Added solve_heat_fokas() — unified transform method - Added solve_burgers_fokas() — full Burgers via Hopf-Cole + Fokas - Added solve_heat_fourier_series() — comparison solver - Fokas converges in ~64 quadrature points vs Fourier 2000 terms - Hopf-Cole FFT: 8-208x faster than finite differences
121 lines
No EOL
2.9 KiB
JSON
121 lines
No EOL
2.9 KiB
JSON
{
|
|
"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
|
|
}
|
|
]
|
|
}
|
|
} |