# Эксперимент: Sparse Multiscale Kernel-Frame Operator (#1191)

{
  "worked": false,
  "confidence": 9,
  "verdict": "Built a compact Wendland kernel-frame encoder/decoder with nested centers, ridge projections, sparse-support diagnostics, and a coefficient-space MLP baseline. Sequential residuals decreased monotonically from 1.0 to 4.47e-6 and then 2.99e-6, with kernel density near 0.12 and finite Gram condition numbers. However, the learned operator reached relative L2 error 0.219 versus 0.176 for the dense pointwise MLP despite using more parameters, so the claimed accuracy advantage was not observed.",
  "metrics": {
    "baseline": "relative L2 0.1762; 37,200 parameters; dense input size 144",
    "idea": "relative L2 0.2193; 92,784 parameters; 252 total multilevel coefficients; kernel density 0.116–0.121; condition numbers 24.3–345.7; training time 3.44 s"
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 kernel_frame_experiment.py",
  "files": [
    "kernel_frame_experiment.py",
    "results.json"
  ],
  "limitations": "Only a small synthetic Fourier-like toy task was tested, not Darcy/elliptic PDE data, FNO/U-Net comparisons, FLOP-matched models, or large-scale sparse memory/speed benchmarks. The first level uses all grid points and nearly reconstructs the input immediately, and the jittered-query metric measures output change rather than error against an analytic target at query points; these limit conclusions about genuine multiscale generalization."
}