Capability Matrix¶

This capability matrix defines the documented evidence boundaries of PhAST. It separates supported and benchmarked pathways from beta, experimental, optional-backend, scaffold, and unsupported features.

For the current plasticity, cohesive interface, and PF-CZM technical-preview boundaries, see the plasticity/interface beta workflow.

Status Definitions¶

Status	Meaning
Supported	Implemented in the public execution pathway and represented by checked-in tests or a reproducible example. The cited evidence remains specific to the documented problem class.
Beta	Mathematically implemented and functional, but robustness or full-domain validation is still under review.
Experimental	Active research pathway with insufficient evidence for general research claims.
Optional backend	Code path exists but requires external solver libraries or specific HPC hardware environments.
Scaffold	Foundational data structures or kernels exist, but the feature is not yet coupled into the global solve.
Unsupported	Feature is mathematically or computationally unsupported.

Simulation Physics¶

Capability	Status	Public Statement
Small-strain 2D linear elasticity	Supported	Exercised through the core mechanics kernels and documented static and quasi-static examples.
Small-strain 1D axial elasticity	Beta	Separate CPU float64 Python API: `line_mesh`, `LineMesh`, and `solve_bar`. Uniform material/area, one left displacement constraint and a right-end force; analytical fields and first-order gradients are tested. See the 1D bar API.
Brittle phase-field fracture, AT2	Supported	Available for explicit dynamics and staggered quasi-static/static solves within the documented examples.
Brittle phase-field fracture, AT1	Beta	Supported via projected damage solves and AT1 threshold fields; benchmark coverage is expanding.
Heterogeneous elastic fields `E(x)`	Supported programmatic path	Per-element fields support structural inclusions and weak/strong bands. The element ordering and low-level authoring route are demonstrated in the heterogeneous-fields teaching example; arbitrary field maps are not currently a general YAML feature.
Heterogeneous fracture fields `Gc(x)`	Supported programmatic path	Per-element fields support weak zones and microstructure-style forward studies through the same heterogeneous-fields teaching example. The example is not a coupled benchmark or material-calibration claim.
Diffuse interface fracture	Beta	Solver-driven weak-interface deflection and strong-interface penetration examples use spatial `E(x)`/`Gc(x)` fields plus AT2 damage solves; discrete cohesive and PF-CZM calibration remain separate.
Plane strain	Supported	Default 2D constitutive setting.
Plane stress	Beta	Available via `material.plane_stress`; formal benchmark coverage is narrower than plane strain.
Spectral / Amor / isotropic energy splits	Supported	Available through `material.energy_split` for brittle phase-field workflows. Plane-stress `spectral` is a reduced 2D in-plane projection; prefer plane-strain `spectral` or plane-stress `amor` where benchmark evidence is required.
`spectral_stress` split	Experimental	Opt-in comparison pathway; do not present it as a generally supported formulation.
Monolithic `(u,d)` L-BFGS solve	Experimental	Research comparison only until the bound-constrained irreversibility algorithms are formalized.
Sparse quasi-static J2 elastoplasticity	Beta	Per-element state, return mapping, commit/rollback, internal force, sparse dispatch, and plastic-work accounting are available; large-mesh backend promotion remains gated.
Ductile PF-plasticity	Beta	Elastic tensile energy plus accumulated plastic-work coupling is implemented, featuring bounded AT2 damage, separated energy ledgers, and guarded staggered support. Benchmark-matched ductile fracture remains gated.
Cohesive elements / discrete CZM	Beta	Stateful true-bilinear cohesive residual/tangent assembly, dissipated-energy history, optional normal-contact penalty, and single-block meshio cohesive-layer insertion are available. ASTM-calibrated structural delamination remains gated.
Coupled brittle PF + cohesive elements	Beta	Staggered AT2 matrix damage plus zero-thickness cohesive-interface delamination exists with matrix notch damage, convergence telemetry, and visual manifests. Calibrated PF-CZM structural validation studies remain gated.
PF-CZM	Beta	Wu PF-CZM is available via `pf_model: PFCZM` for forward nonlinear damage solves with tensile-strength-calibrated rational degradation and uniaxial validation. Structural crack-growth and PF-plasticity-cohesive coupling remain gated.
Coupled PF + plasticity + cohesive interfaces	Unsupported	Not currently supported within the public workflow surface.
Learned damage proposal	Experimental	A user-supplied predictor may provide a projected initial guess; the classical damage solve remains authoritative. No trained model is distributed.
Audited learned damage replacement	Experimental	A predicted damage state may replace one damage solve only after bound, irreversibility, phase-field boundary-condition, and projected-residual checks. Rejection uses the classical fallback by default.
3D fracture	Unsupported	The documented fracture element pathways are two-dimensional.
P2 / Q8 / Q9 element primitives	Scaffold	Shape functions, quadrature, and single-element stiffness tests exist for higher-order families; global solver dispatch is not supported.
Native Q4 isotropic mechanics + AT2 damage	Beta	Structured Q4 mesh helpers, native Q4 mesh admission, 2x2-Gauss isotropic mechanics, SciPy/MUMPS sparse-direct stiffness assembly, and matrix-free Q4 AT2 damage are tested. Q4 PF-CZM, AT1, and plasticity remain gated.

Solvers and Backends¶

Capability	Status	Public Statement
Explicit dynamics, Velocity Verlet	Supported	Principal documented pathway for dynamic impact and fracture simulations.
Staggered quasi-static/static solve	Supported	Principal documented implicit brittle-fracture pathway, using `jacobi` as the conservative damage preconditioner. Matrix-free CG and sparse-direct mechanics backends are available.
Rotation-free connectors in `quasi_static`	Beta	The staggered call forwards active connectors to the existing reduced mechanics solve. CPU float64 isotropic elastic tests check connector kinematics, reaction and moment balance. Nonlinear fracture trajectories require separate case-specific verification.
`quasi_static_legacy` secant path	Beta	Retained strictly for compatibility and selected MPC/frozen-secant workflows.
SciPy SuperLU sparse direct baseline	Supported	Portable sparse-direct baseline when SciPy is installed.
PETSc/MUMPS	Optional backend	Runtime-guarded. When available, `backend='auto'` prioritizes this for CPU sparse-direct mechanics.
cuDSS / nvmath	Optional backend	Runtime-guarded. GPU sparse-direct path requires current nvmath/cuDSS validation on the target hardware stack.
AMG / AmgX / GMG damage preconditioning	Experimental	Performance-oriented pathways for quasi-static fracture; use Jacobi unless the alternative preconditioner is itself part of the study.
Anderson acceleration	Beta	Available for staggered iterations; use only with benchmark-specific validation.

Inverse Workflows¶

Capability	Status	Public Statement
Differentiable forward sensitivities	Beta	Supported tensor operations can participate in PyTorch autograd, but nonsmooth history, bounds, and active-set switches require case-specific interpretation.
Public inverse-analysis examples	Scaffold	`examples/inverse_problems_beta/` is a README-only landing zone until promoted inverse examples include configs, losses, retained lightweight outputs, and validation notes.
General-purpose inverse-calibration framework	Unsupported	The public release does not provide a turnkey inverse-problem framework for arbitrary observations, priors, or optimizers.

Selected paper-specific inverse figures have separate retained-data reproduction commands. Their catalogue distinguishes replotting saved results from running the inverse calculation. These utilities preserve the scope of the recorded studies while the complete companion archive is prepared.

Declarative YAML Workflows¶

Capability	Status	Public Statement
YAML problem definition	Supported	Primary execution entry point (e.g., `python -m phast run config.yaml`).
YAML schema validation	Supported	`--validate-only` enforces schema compliance and reports line-numbered semantic errors.
`explain-config` review	Supported	Prints selected physics, solver paths, provenance, and setup warnings without initiating meshing or solving.
`schema_version`	Supported	Current runnable configs declare `schema_version: 1`; legacy files trigger review warnings.
Resolved run lockfile	Supported	Execution generates `run_lockfile.json` capturing the config hash, resolved objects, CLI arguments, and Git state.
Built-in geometry generators	Supported	Available through `geometry.type` and `geometry.parameters`.
External meshes	Beta	Supported via `geometry.mesh_path`; node-set capability relies on the specific mesh format standard.
Declarative primitive geometry DSL	Beta	Parsed by selected benchmark configs; broader geometry coverage remains under evaluation.
Config inheritance / sweeps	Unsupported	Parameter sweeps currently require external scripting or duplicated declarative files.
JSON Schema export / IDE autocomplete	Supported	`python -m phast schema` exports the schema used for editor assistance and external validation.

Outputs and Validation Artifacts¶

Capability	Status	Public Statement
Zarr trajectory stores	Supported	Principal high-fidelity format for trajectory workflows; chunked and appendable.
HDF5 snapshots	Legacy	Maintained for backward compatibility and benchmark extraction; deprecated for new large-scale training corpora.
VTU / PyVista-style visualization	Beta	Available via declarative output settings; format fidelity relies on optional visualization dependencies.
Automated visualization generation	Beta	Generates documentation-ready GIFs and plots; artifacts must be manually verified before academic publication.
Reaction-force logging	Supported	Available for load-displacement verification through `output.reaction_node_set` and `output.reaction_component`.
Strict-parity benchmark scripts	Beta	`compare.py` routines available for selected examples to verify tolerances against reference literature.
CPU execution and optional accelerator use	Supported	Core CPU execution is exercised by public checks. Practical device choice for larger simulations depends on mesh size, precision, backend availability, and the documented workflow.