Module surrogate 

Forward-model surrogates for multi-isotope accelerated fits.

Currently exposes SparseEmpiricalCubaturePlan — a Jacobian-anchored sparse empirical cubature on the joint σ-pushforward manifold. Round-2 of the algorithm-design round-robin (contestant codex04) validated this as the k ≥ 2 winner; see .research/algo_design_roundrobin_r2/JUDGMENT.md and the independent cross-family JUDGMENT_CODEX.md.

Mathematical basis

Let R be the resolution operator on a fixed target grid, σ_1(E'), …, σ_k(E') the per-isotope cross-sections, and x_ℓ = (σ_1(E'_ℓ), …, σ_k(E'_ℓ)) ∈ ℝ^k the pushforward of a source point E'_ℓ. For each row i, exact evaluation is

T_i(n) = Σ_ℓ R_{iℓ} exp(-n · x_ℓ)
∂T_i/∂n_j = -Σ_ℓ R_{iℓ} x_{ℓ,j} exp(-n · x_ℓ)

The row support contains ~82 ℓ’s on the VENUS 3471-bin production grid. By [Carathéodory / Tchakaloff], any nonneg combination of feature vectors over this support is matched (in feature space) by an equivalent nonneg combination supported on at most d + 1 atoms, where d is the feature dimension. Choosing features = forward evaluations at S training densities + Jacobian evaluations at one anchor density gives d = S + k features, so each row collapses to ≤ S + k + 1 atoms while preserving positivity, row-stochasticity, and the exact Jacobian at the anchor.

Empirical compression (real VENUS operator, codex04 measurements)

Scenario	k	avg atoms/row	max atoms/row	compression vs exact
Hf (natural group)	1	3.53	67	23.3×
Hf + W	2	5.65	7	14.5×
U-235 + U-238	2	5.32	7	15.5×
Gd + Eu + Sm	3	8.59	9	9.6×
Hf-174/176/177/178/179/180 indep.	6	9.03	15	9.1×

LP solver

Row-wise Tchakaloff reduction is framed as a feasibility LP (minimize 0 subject to the equality constraints) and solved with microlp. The problem is small (≤ S + k + 1 rows × |support| columns, here typically ~ 10 × ~ 100) so a pure-Rust simplex is fast enough.

Structs

ScalarChebyshevPlan

Chebyshev-in-density interpolant of T_i(n) for scalar (k = 1) forward models. For each row i, pre-samples T_i(n_j) at M Chebyshev-of-the-first-kind nodes in [0, n_max], then stores the Chebyshev coefficients. Online evaluation is Clenshaw recurrence with M multiply-adds per row.

SparseEmpiricalCubaturePlan

Row-wise Tchakaloff cubature of the joint σ-pushforward measure on a fixed target grid.

Enums

CubatureBuildError

Errors from SparseEmpiricalCubaturePlan construction.

ScalarSurrogateBuildError

Errors from scalar surrogate plan construction.

Functions

fingerprint_f64_slice

FNV-1a-64 hash of an f64 slice by bit pattern — used for scalar-surrogate dispatch’s σ-identity check.

Type Aliases

ScalarSurrogatePlan

Scalar (k = 1) surrogate used by the downstream dispatch layers (see TransmissionFitModel / PrecomputedTransmissionModel).