# Эксперимент: Measurement-Space Neural Operator with Mesh Transfer (#862)

{
  "worked": true,
  "confidence": 7,
  "verdict": "Built a coordinate-aware measurement-space surrogate with permutation-invariant sensor encoding and arbitrary-coordinate decoding, plus a fixed-grid MLP baseline. The mechanism checks manifested: permutation changes produced only 1.04e-7 maximum prediction difference, output discrepancy scaled approximately linearly with reconstruction perturbation (correlation 0.994), and reconstruction RMSE fell from 0.851 at 4 sensors to 0.0373 at 64 sensors. The practical mesh-transfer win was not observed: transferred RMSE was 0.768–0.827 versus 0.646 for the fixed-grid baseline, so the evidence supports the mechanism but not improved accuracy in this toy setup.",
  "metrics": {
    "baseline": "Fixed-grid MLP: RMSE 0.6457 on canonical 32-sensor/fixed-grid evaluation.",
    "idea": "Measurement-space model: arbitrary-mesh RMSE 0.7766 (8 sensors), 0.7751 (16), 0.8267 (32), 0.7677 (64); permutation max difference 1.04e-7; perturbation/discrepancy correlation 0.9936; reconstruction RMSE 0.8510/0.6854/0.2737/0.1014/0.0373 for 4/8/16/32/64 sensors."
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py",
  "files": [
    "experiment.py",
    "results.json"
  ],
  "limitations": "This is a small synthetic 1D Fourier-field experiment, not Darcy, Burgers, or a 2D neural operator. The transfer model and baseline were not matched exactly in parameter count or training objective; no learned reconstruction decoder or explicit beta consistency loss was implemented, and speed/FLOP scaling, 16x16/32x32/64x64 2D meshes, and retraining-free distribution-shift robustness were not tested."
}