# Эксперимент: Resolution-aware operator data budget (#1314)

{
  "worked": true,
  "confidence": 8,
  "verdict": "Built a compact kernel-based two-stage operator-learning MVP with exact-output cubic reconstruction, learned offline kernel regression, fill-distance verification, a fixed-N baseline, and N=ceil(m^kappa) schedules. The math check reproduced uniform fill distance h=1/(2(m-1)) to numerical precision with log-log slope -1.09. In the toy operator, fixed N=16 stagnated at errors 0.720, 0.727, 0.728 for m=16,32,64, while kappa=1.0 improved to 0.720, 0.632, 0.470 and kappa=1.5 reached 0.471, 0.310, 0.311; the oracle error fell from 0.204 to 0.0142 to 0.000385. This is a clear qualitative signal supporting resolution-aware data growth, but not evidence of superiority at equal compute because larger N costs more.",
  "metrics": {
    "baseline": "Fixed N=16 learned relative L2 error: m=16 0.7202, m=32 0.7273, m=64 0.7276; wall time approximately 0.162-0.164 seconds.",
    "idea": "For kappa=1.0, N=16,32,64 gives relative L2 errors 0.7202, 0.6322, 0.4700; for kappa=1.5, N=64,128,128 gives 0.4710, 0.3099, 0.3113. Oracle errors are 0.2040, 0.01424, 0.000385."
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 resolution_budget_experiment.py",
  "files": [
    "resolution_budget_experiment.py",
    "results.json",
    "rerun_output.txt"
  ],
  "limitations": "This is a small synthetic smooth operator and kernel regressor rather than an FNO, DeepONet, or PDE benchmark. The kappa=1.5 schedule is capped at N=128 at m=64, only one random train/test split was used, wall-clock measurements are noisy, and no equal-FLOP comparison or GPU run was performed."
}