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