dfsc Roadmap

This roadmap separates implemented functionality from research extensions. It is intended to keep the software claim precise while making the ecosystem direction reproducible.

Implemented Core

  • PyTorch dfsc package as the only public library namespace.
  • Differentiable Mittag-Leffler spectral layer for retained real spectra.
  • Trainable alpha and beta through PyTorch autograd.
  • 1D/2D tensor-product Dirichlet, Neumann, periodic, and mixed constructors.
  • Symmetric PSD operator and graph-Laplacian adapters for user-supplied discretizations.
  • Problem--algorithm--solution interface through dfsc.solve.
  • Automatic direct/stable routing with numerical diagnostics and solution retcodes.
  • Generalized stiffness/mass operator adapter with mass-aware projection.
  • First history-aware implicit L1 fallback for constant-order linear Caputo systems.
  • Fully reorthogonalized Lanczos matrix-function action with an embedded subspace-disagreement diagnostic and automatic size-based routing.
  • Sparse tensor and matrix-free self-adjoint operator contracts with differentiable matvec parameters and CUDA validation.
  • Direct and FFT Caputo-L1 full-trajectory derivative operators with automatic length-based routing, analytic convergence checks, and CUDA gradients.
  • Controlled complex Mittag-Leffler series and Arnoldi actions for moderate reduced radii, including non-normal diagnostics and complex CUDA validation.
  • Semilinear mild-form Picard problem with explicit convergence retcodes.
  • Forced-dynamics wrapper, inverse-order workflow, hybrid residual workflow.
  • Scoped application cases for anomalous diffusion, assembled linear relaxation, network memory diffusion, and periodic fractional advection--diffusion.
  • CPU/GPU smoke tests, unit tests, and synthetic experiment scripts.
  • Single distributable dfsc namespace and a 95% pre-release internal gate.
  • Numerical reliability reports for real and controlled complex evaluation and solver outputs.

Experimental Extensions

  • dfsc.VariableOrderMLSL: direct-query wrapper using one alpha per query time.
  • dfsc.DistributedOrderMLSL: differentiable quadrature mixture over alpha nodes.
  • dfsc.mlsl_applicability_report: machine-readable check for the current spectral assumptions.
  • dfsc.validate_dataset_manifest: provenance-first contract for future public physical benchmark datasets.

These extensions are useful for early SciML experiments. They do not yet make dfsc a general variable-order or distributed-order fractional solver library.

Near-Term Milestones

  1. Publish a versioned source release and wheel.
  2. Deploy the existing API documentation as a hosted site.
  3. Add a second public physical benchmark with an explicit redistribution license.
  4. Promote experimental wrappers after accuracy and stability validation.
  5. Add compatibility examples with a neural-operator workflow.
  6. Add block/preconditioned Krylov/Arnoldi, contour actions, and online fast-memory CQ/SOE time-stepping algorithms.

Longer-Term Research Milestones

  • Large-radius complex-spectrum operators with contour/rational error control.
  • Variable-order formulations with history-aware validation.
  • Distributed-order kernels with calibrated quadrature rules.
  • Mesh/discretization adapters for sparse and matrix-free irregular-domain workflows.
  • Optional JAX or Julia backend interoperation.