Benchmarks

Kuramoto Kernel — Python vs Rust Speedup

Honest comparison: NumPy SIMD dominates at mid-range N. Rust advantage emerges at scale where cache locality and manual vectorisation win.

N (oscillators)	Python (NumPy)	Rust (PyO3)	Speedup	Notes
64	2.1 µs	0.12 µs	17.3×	Small N: Rust call overhead negligible, NumPy dispatch overhead dominates
256	4.8 µs	5.3 µs	0.9×	Parity zone — NumPy BLAS/SIMD wins on contiguous sin/cos
1,000	38 µs	27 µs	1.4×	Rust pulls ahead as matrix grows beyond L1 cache
4,096	580 µs	320 µs	1.8×	Cache-conscious tiling in Rust crate
16,384	9.2 ms	4.0 ms	2.3×	L2/L3 pressure; Rust avoids Python object overhead
65,536	147 ms	58.8 ms	2.5×	Peak advantage at large scale

16-Layer K_nm UPDE PAC Benchmark

909 µsPAC γ=1.0

811 µsNo PAC γ=0

12%PAC Overhead

16×16K_nm Matrix

PAC (Phase-Amplitude Coupling) gating adds 12% overhead for full γ=1.0 coupling. Acceptable trade-off for biologically-motivated cross-layer synchronisation.

Lyapunov Stability vs ζ (External Driver)

ζ	λ_max	Stability	Regime
0.0	-0.0023	Stable	Free oscillation
0.5	-0.0018	Stable	Weak entrainment
1.0	-0.0011	Stable	Moderate coupling
2.0	-0.0004	Marginal	Strong coupling
5.0	+0.0031	Unstable	Forced desynchronisation
10.0	+0.0089	Divergent	Chaotic regime

GK Linear Benchmarks

Cyclone Base CaseReference

R/L_T=6.9, κρ_i=0.3. Growth rate γ=0.175 v_th,i/L_n. Matches GS2/GENE within 5%. 512-point velocity grid, 32 poloidal modes.

SPARC Mid-RadiusValidated

r/a=0.5, B_T=12.2 T. ITG dominated. γ_max=0.21 v_th,i/L_n at k_θρ_i=0.4. TEM subdominant. Ion-scale only.

ITER Mid-RadiusValidated

r/a=0.5, B_T=5.3 T, β=2.5%. Mixed ITG/TEM. γ_max=0.14 v_th,i/L_n. E×B shear stabilisation active.

PPO Reinforcement Learning Training

Cloud Training Results

500K environment steps on Vertex AI T4. Gymnasium-compatible tokamak environment. 3 baselines compared on cumulative reward over 1000-step episode.

143.7PPO Reward

58.1MPC Reward

-912.3PID Reward

500KTraining Steps

0%Disruption Rate