Generality Validation

The current MLSL component can be tested for primitive-level generality, but the claim should be stated carefully.

What We Validate

The validation matrix checks whether the same component works across:

• 1D and 2D Dirichlet spectral domains.
• Subdiffusive and superdiffusive temporal orders.
• Multiple spatial fractional orders.
• Low-mode, multi-mode, localized, and batched initial conditions.
• Forward evaluation, differentiability with respect to alpha and beta, linearity, batch consistency, and inverse recovery.

Run:

python experiments/exp21_primitive_generality.py

Outputs:

results/tables/primitive_generality_matrix.csv
results/primitive_generality_summary.json

Current Result

The current stable-configuration run passes 34 of 34 checks.

This supports the claim that MLSL is already a reusable SciML primitive in moderate regimes: it is not limited to one initial condition, one parameter choice, one dimension, or one task type.

Observed Boundary

Earlier default-series runs exposed an important limitation rather than invalidating the direction:

• For alpha=0.65, beta=2.0, the default power-series branch gives finite forward outputs but non-finite gradients in some stiff settings.
• Joint recovery of alpha and beta from a single low-frequency mode is weakly identifiable, so the validation now tests alpha-only recovery for single-mode data and joint recovery for multi-mode data.

Interpretation

The stable configuration has demonstrated broad empirical portability across the current validation matrix. The next primitive-level milestone is to expand this matrix to harder PDE families, larger batches, longer times, GPU execution, and repeated random seeds.