Kinetic transport inversion

What it measures: the end-to-end application the truncated adjoints exist for — recovering a collisionality profile of a spectral kinetic ladder from truncated low-moment observations by damped Newton, with gradient and Hessian flowing through the bounded adjoint. See Block-tridiagonal solvers.

Reproduce:

python -m benchmarks.benchmark_kinetic_inversion --json

Records: benchmarks/results/kinetic_inversion.json (CPU) and benchmarks/results/gpu/ (A4000; physics_scale_a2.json for the large-scale generated-block run).

Inversion (m=36, N=96)

Damped Newton converges quadratically to the exact profile — loss 4.7e-2 → 1.6e-14 in eight steps, recovered (nu0, a) = (1.0, 0.6) exactly, adjoint gradient validated against finite differences (identically on CPU and GPU). The extended-profile misfit Hessian spectrum {3e-10, 1e-5, 1.5e-1} shows the quadratic coefficient is unidentifiable from truncated moments — the adjoint machinery diagnoses observability for free.

Physics scale on GPU (m=195, generated blocks)

With the generated-block bounded adjoint (block_thomas_truncated_fn(params=..., adjoint_window=8)) at the drift-kinetic block size m=195:

N_modes	gradient scratch	naive tape (estimate)
256	33.7 MiB	0.9 GB
1024	33.7 MiB	3.7 GB
4096	33.7 MiB (flat)	14.9 GB — exceeds the 16 GB card

The largest gradient is computable only through the bounded adjoint on this hardware. A further observability finding comes with it: the profile slope’s effect on the observed low moments shrinks like 1/N_modes, so at physics scale only the local low-mode collisionality is recoverable — Newton pins nu0 to 0.9972 across all sizes while the slope direction is a near-flat valley. Truncated observations bound both the memory and the information.

Three-path memory record (CPU, m=36)

N	naive tape	array-band bounded	generated bounded
32	3.0 MiB	2.4 MiB	1.71 MiB
256	23.5 MiB	9.2 MiB	1.71 MiB
512	46.8 MiB	17.0 MiB	1.71 MiB (flat)