Эксперимент: FMM-Accelerated Polyharmonic Neural Field Head (#856)

{ "worked": true, "confidence": 8, "verdict": "Built a reproducible PHS interpolation head with exact polynomial null-space projection, projected PCG, a Vecchia-style Matérn preconditioner, and chunked query evaluation. The core predictions were confirmed: projected k=2 PHS interactions scaled as rho^2 with maximum error 3.6e-15, projected squared-distance polynomial terms vanished at 3.1e-15 relative magnitude, and computed weights satisfied the polynomial constraint near 1e-14. Vecchia preconditioning reduced PCG iterations from 292 to 196, but did not reach the paper-scale fewer-than-20-iteration target; this is a promising small-scale signal rather than a demonstrated FMM speedup.", "metrics": { "baseline": "Unpreconditioned projected PCG: 292 iterations, relative residual 7.65e-08; dense query evaluation: 0.00288 seconds.", "idea": "Vecchia-preconditioned projected PCG: 196 iterations with m=16 or 32, relative residual 3.83e-08 to 6.32e-08; exact-vs-chunked query error 0.0. Scaling sweep observed [0.25, 1, 4, 16] versus predicted rho^2 [0.25, 1, 4, 16]." }, "how_to_run": "OMP_NUM_THREADS=1 OPENBLAS_NUM_THREADS=1 MKL_NUM_THREADS=1 /home/maxwelhelp/main/bin/python3 phs_experiment.py", "files": [ "phs_experiment.py", "results.json", "results_corrected.json" ], "limitations": "This MVP uses dense scipy kernel construction and multiplication rather than a true FMM, tests only n=180 in 2D and one synthetic function, and implements a simplified Vecchia precision rather than the paper's full reverse-Cholesky construction. It does not test 10k-1M anchors, GPU execution, peak-memory scaling, neural coordinate encoders, or a rigorous wall-clock FMM comparison." }