dfsc Ecosystem Maturity

dfsc is developed as a specialized tool-algorithm library for differentiable Mittag-Leffler spectral learning. Its design borrows the problem/algorithm separation common in mature scientific-computing ecosystems, while keeping a strict scope: known or user-supplied spectral propagators with differentiable fractional parameters.

Current Maturity Layer

Passing the repository audit means the research artifact is internally consistent; it does not mean that dfsc has reached the release maturity or equation coverage of long-lived public solver ecosystems.

Layer Current state Remaining gap
Package identity Single public namespace: dfsc Public release and hosted docs
Internal release gate 20/20 pre-release checks pass External adoption and public history
Core primitive Batched PyTorch real-negative MLSL plus controlled moderate-radius complex evaluation Large complex sectors and certified complex error control
Algorithms Direct, stable, forced, Lanczos, controlled Arnoldi, FFT Caputo-L1 history, operator, graph, generalized operator, semilinear Picard, and L1 fallback Contour/rational methods and online fast-memory algorithms
Problem interface Spectral, graph, assembled operator, forced, semilinear, linear Caputo L1, and four scoped application templates Standardized inverse and variable-order problem templates
Solution object Values, time axis, retcode, warnings, stats, and selection diagnostics Serialization and richer error estimates
Numerical routing AutoDFSC and diagnostic Mittag-Leffler evaluation Calibrated rules over wider verified regimes
Autograd/GPU Tested for alpha/beta, matrix-free, nonlinear, and FFT-history gradients on CUDA Larger multi-GPU and mixed-precision profiling
Reliability contract Validated-domain, convergence, gradient, and empirical error metadata Rigorous global error bounds
Data evidence One experimental H-actin SPT condition with provenance, checksum, five trajectory splits, and model comparisons Explicit redistribution permission and independent physical modalities
Experimental orders Variable-order and distributed-order wrappers Systematic theory and large-scale validation

Intended Differentiation

dfsc is not yet a general fractional solver library. Its primary path remains Mittag-Leffler spectral propagation, while the constant-order linear Caputo L1 solver establishes the first explicit history-aware fallback path.

The main differentiator is not solver breadth. It is the ability to expose that propagator as a differentiable layer, algorithm object, and solution-producing workflow inside PyTorch.

The current center of application coverage is anomalous transport and linear fractional relaxation. Around that center, the same primitive now supports assembled finite-element systems, graph diffusion, and controlled non-self-adjoint advection--diffusion. Each template carries machine-readable assumptions and limitations rather than implying general domain coverage.

Next Maturity Milestones

  1. Resolve redistribution permission for the integrated SPT data and add a second benchmark with an explicit open-data license.
  2. Add an ecosystem comparison script against at least one PINN/fPINN workflow and one fractional numerical solver on the same task.
  3. Add block Krylov/Arnoldi and preconditioning strategies for larger batches and stiff spectra.
  4. Add contour/rational complex actions and an online fast-memory CQ/SOE time stepper before promoting broader solver claims.
  5. Promote experimental order wrappers only after accuracy and stability tests.
  6. Publish a versioned source archive, wheel, and hosted API documentation.