Explicit custom backward for the truncated series branch.
History-free spectral layer with differentiable alpha and beta.
1D and 2D Dirichlet spectral constructors.
Stable preset via MLSLConfig.stable() for broader negative-real spectral
regimes.
1D Neumann spectral constructor in addition to 1D/2D Dirichlet constructors.
1D periodic and mixed-boundary spectral constructors.
2D Neumann, periodic, and mixed-boundary tensor-product constructors.
Batched forward evaluation for dataset-level use.
Baselines and experiment suite covering FNO, DeepONet, fPINN, OOD alpha,
sparse inverse recovery, 2D inverse recovery, and runtime scaling.
Unit tests for layer shapes, gradients, hybrid finite values, and 2D use.
Examples for quickstart, batched evaluation, and inverse alpha/beta recovery.
Primitive generality matrix across dimensions, fractional orders, initial
conditions, batching, gradients, and inverse recovery.
Paper-grade extension suite covering long horizons, repeated seeds, batch and
device profiling, stronger neural baselines, forcing, fPINN repetition, and
proposition-level timing evidence.
Manufactured-solution validation for the forced MLSL component in a multi-mode
spectral regime.
Boundary-condition generality checks for 1D Dirichlet and Neumann settings.
Extended boundary-condition generality checks for 1D Dirichlet, Neumann,
periodic, and mixed settings.
High-precision reference checks for the hybrid two-parameter Mittag-Leffler
evaluator.
Shifted-spectrum linear reaction-diffusion family experiment.
Semilinear cubic-reaction backbone experiment using MLSL as the linear
history-free primitive.
Larger multi-seed neural baseline experiment.
CUDA validation on RTX 5070, including CPU/GPU consistency, batch profiling,
and half-precision capability probes.
Diagnostic one-/two-parameter Mittag-Leffler evaluation with embedded
truncation disagreement and branch counts.
True direct/stable algorithm reconfiguration plus automatic regime selection.
Generalized symmetric stiffness/mass spectral problems with mass projection.
Differentiable constant-order linear Caputo L1 history fallback.
Dense symmetric-PSD Lanczos Mittag-Leffler matrix-function action, including
batched initial states, automatic size-based selection, and empirical
subspace-disagreement diagnostics.
Sparse tensor and matrix-free self-adjoint operator paths, including
differentiable operator parameters, N=4096 validation, and CUDA execution.
FFT-accelerated Caputo-L1 full-trajectory history convolution, including
direct-reference agreement, analytic power-law convergence, gradients,
N=65536 execution, and CPU/GPU consistency.
Controlled complex-argument Mittag-Leffler evaluation and Arnoldi actions for
general operators, validated against mpmath, high-precision matrix series,
finite differences, matrix exponentials, and CUDA complex128.
Domain-oriented application cases for regular-domain anomalous diffusion,
assembled finite-element relaxation, graph memory diffusion, and controlled
periodic fractional advection--diffusion. Each case reports its recommended
algorithm, differentiable parameters, assumptions, and limitations.
Experimental H-actin SPT evidence chain with 3,112 trajectories,
trajectory-level leakage control, traditional and neural baselines, five
splits, and an MLSL-residual regression component. Raw-data redistribution
remains pending because the source page does not state a license.
Semilinear mild-form Picard solver with convergence diagnostics, non-success
retcodes, and autograd through fractional and nonlinear parameters.
Single-package dfsc source layout; the legacy mlsl distribution has been removed.
Machine-readable numerical reliability reports and strict validated-domain evaluation.
A 20-check pre-release internal readiness gate covering numerical, API, test,
application, documentation, and packaging evidence.
Still Needed For Paper-Grade Primitive
More accurate stable Mittag-Leffler evaluator with reference validation over
wider long-time and stiff regimes.
Contour or rational evaluation beyond the current conservative complex
radius, including non-normal and pseudospectral error analysis.
Wider reference validation for the hybrid two-parameter Mittag-Leffler
evaluator in stiffer forced dynamics and larger negative arguments.
Larger GPU profiling for full baseline training workloads.
Broader nonlinear or variable-coefficient PDE families beyond linear spectral
cases.
Broader nonlinear solvers beyond the current fixed-point mild formulation.