Эксперимент: Block-TT 3D Neural Operator (#1044)

{ "worked": true, "confidence": 8, "verdict": "The core mechanism manifested: TT application matched dense multiplication to approximately 3e-15 relative error, requested SVD tolerances produced errors below their bounds, and increasing TT rank reduced approximation error while storage grew approximately quadratically in the interior rank. However, the small random toy did not show a practical memory win: block storage exceeded dense storage at the tested accuracy, so the result supports mathematical correctness but not a demonstrated end-to-end advantage.", "metrics": { "baseline": "Dense 128x128 operator: 16,384 parameters and exact reference multiplication.", "idea": "TT application relative error 2.87e-15; tolerance-sweep errors 0.273, 0.0897, and approximately 3.3e-15 for relative tolerances 0.5, 0.2, and <=0.1; rank-32 TT used 10,512 parameters at 0.524 relative error; separate blocks used 18,432 parameters at approximately 2.8e-15 reconstruction error." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 run_experiment.py", "files": [ "block_tt3d.py", "run_experiment.py" ], "limitations": "No neural-network training, GPU benchmark, 64^3 workload, throughput measurement, optimizer-time rounding, CP/tensor-ring comparison, or PDE/Navier-Stokes validation was tested. The block experiment used a small 2x4x4x4 grid and synthetic random operators, so practical scalability and learned-operator accuracy remain unverified." }