# Эксперимент: Singularity-Enriched Neural Ansatz (#1276)

{
  "worked": true,
  "confidence": 8,
  "verdict": "Built a differentiable singularity-enriched neural ansatz with a smooth cutoff, learned amplitude, fixed lambda=1/2 mode, and corner-focused sampling. The numerical math check recovered log-log slope 0.500 exactly, while grading increased the fraction of points within r<0.12 from 1.12% to 8.79%. At equal 1,600 training points, enriched+graded reduced global relative L2 error from 1.475% for the uniform baseline to 0.826%, and reduced corner relative error from 21.5% to 2.90% (about 7.4x better), so the local regularity-bottleneck effect is real in this toy setting.",
  "metrics": {
    "baseline": "Uniform MLP: global relative L2=0.01475, corner relative L2=0.2151, train MSE=4.93e-5. Graded baseline: global=0.01990, corner=0.1274.",
    "idea": "Enriched uniform: global relative L2=0.009733, corner relative L2=0.08864. Enriched+graded: global=0.008257, corner=0.02901, train MSE=1.39e-5. Math slope=0.500 versus lambda=0.5; near-corner sampling fraction=0.08791 versus 0.01123 uniform."
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py",
  "files": [
    "experiment.py",
    "results.json"
  ],
  "limitations": "This is a manufactured scalar regression rather than a full mixed-boundary elasticity or Poisson PINN with PDE residuals. The angular mode and exponent were supplied analytically, only one fixed seed and one sample budget were tested, and no wall-clock or FLOP-normalized comparison was recorded. The global improvement was less than the suggested 2x threshold, although the corner improvement was substantially larger."
}