# Эксперимент: Chebyshev-Stabilized SDIRK Neural ODE (#1368)

{
  "worked": false,
  "confidence": 9,
  "verdict": "Built a five-stage SDIRK4 solver with Chebyshev inner iterations, fixed-point control, and explicit RK4 comparison on a 16-dimensional stiff diagonal ODE. The literal recurrence from the idea diverged dramatically, with residual ratio 2.70e17, contradicting the claimed contraction; a dimensionally corrected momentum term reduced the residual by about 1/728 and enabled stable large-step propagation, but that is not the stated algorithm. Therefore the authoritative idea was not validated as written.",
  "metrics": {
    "baseline": "At h=0.2, fixed-point stage residual ratio 9.40e33 and propagation error Infinity; RK4 error 9.50e7.",
    "idea": "Literal Chebyshev residual ratio 2.70e17 and propagation diverged; corrected recurrence had residual ratio 1.37e-3 and h=0.2 propagation error 0.228."
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py",
  "files": [
    "experiment.py",
    "results.json"
  ],
  "limitations": "Only a linear diagonal stiff toy system was tested; no neural ODE training, nonlinear Jacobian estimation, GPU execution, Newton baseline, wall-clock/FLOP comparison, or gradient/backward behavior was evaluated."
}