Validation status¶
Generated by scripts/build_method_status.py --public from pinneapple_catalog/methods.py and pinneapple_catalog/method_status.json (test scan of 2026-10-17). Do not edit by hand.
Rule. An item is validated when at least one test function that exercises it compares the result with an independent reference (closed-form or manufactured solution, published or tabulated value). Tested means it has tests, none of which compares with a reference. Only validated items are in pinneapple_catalog.validated_methods(). Every status lists its evidence in method_status.json.
| Category | Validated | Tested, no reference | No test |
|---|---|---|---|
| Solvers | 31 | 8 | 2 |
| Training methods | 2 | 12 | 8 |
| Physical equations | 50 | 18 | 3 |
| Physical problems | 27 | 9 | 30 |
| All | 110 | 47 | 43 |
Solvers¶
| Id | Item | Status | Reference tests | Other tests |
|---|---|---|---|---|
| S1 | Finite differences 1D/2D/3D | ✅ validated | 2 | 11 |
| S2 | Finite elements (linear) + nonlinear beam FEM | ✅ validated | 6 | 15 |
| S3 | Finite volumes | ✅ validated | 2 | 2 |
| S4 | Spectral (Fourier pseudo-spectral) | ✅ validated | 3 | 2 |
| S5 | Lattice Boltzmann D2Q9 / D3Q19 (+ Smagorinsky LES) | ✅ validated | 2 | 21 |
| S6 | SPH / ISPH / DFSPH | ⚪ no test | 0 | 0 |
| S7 | Meshfree RBF collocation (Kansa) | ✅ validated | 1 | 1 |
| S8 | X-TFC (IVP, PDE, subdomains) | ✅ validated | 4 | 8 |
| S9 | Discrete-time PINN / implicit Runge-Kutta Gauss-Legendre | 🟡 tested, no reference | 0 | 2 |
| S10 | Stiff kinetics ODE | ✅ validated | 1 | 0 |
| S11 | TVD advection | ✅ validated | 1 | 0 |
| S12 | Immersed boundary (FDM) | ⚪ no test | 0 | 0 |
| S13 | Beam BVP FDM / 3D elasticity FDM | ✅ validated | 2 | 0 |
| S14 | Eddy current FDM | ✅ validated | 3 | 3 |
| S15 | Bekker-Wong terramechanics | ✅ validated | 1 | 19 |
| S16 | N-body (REBOUND) | ✅ validated | 1 | 2 |
| S17 | JAX-CFD | 🟡 tested, no reference | 0 | 3 |
| S18 | Particle dynamics: rigid body, MPM, molecular dynamics | 🟡 tested, no reference | 0 | 13 |
| S19 | Signal decomposition: CEEMDAN, EEMD, VMD, HHT, SSA, SST, STL, FFT, wavelet | 🟡 tested, no reference | 0 | 1 |
| S20 | Co-simulation (graph + engine, algebraic loops by Tarjan SCC) | 🟡 tested, no reference | 0 | 11 |
| S21 | Digital twin state estimation: KF/EKF/UKF/EnKF, prognostics, signal reconstruction | 🟡 tested, no reference | 2 | 39 |
| S22 | 1D process components (pipe network, transient pipe, heat exchanger, valve, reaction, polytropic path, compressor map) | 🟡 tested, no reference | 0 | 3 |
| S23 | Explicit equation-system solver (evaluation order) | 🟡 tested, no reference | 0 | 1 |
| S24 | External solvers: OpenFOAM, FEniCS, ANSYS/CFD formats, MATLAB, Modelica/FMI, MuJoCo, Genesis, TurboDesigner | ✅ validated | 1 | 80 |
| S25 | Causal telemetry conditioning (Hampel one-step, rate limit, first-order filter, gaps) | ✅ validated | 1 | 6 |
| S26 | 2D shallow-water finite volumes (MUSCL + HLL, wet/dry, walls, gates, virtual sensors, health checks) | ✅ validated | 1 | 3 |
| S27 | ETDRK4 exponential integrator for stiff semilinear PDEs (contour phi-functions, blow-up guard) | ✅ validated | 5 | 1 |
| S28 | Stable fluids 2D (semi-Lagrangian advection, spectral projection, vorticity confinement) | ✅ validated | 2 | 4 |
| S29 | 2-D A_z magnetostatics, P1 FEM with Newton (nonlinear B-H, magnets, (anti-)periodic constraints) | ✅ validated | 1 | 6 |
| S30 | Time-harmonic 2-D eddy currents (A_z, solid conductors with imposed net currents) | ✅ validated | 1 | 1 |
| S31 | Surface-PM machine model: Maxwell-stress and co-energy torque, cogging, back-EMF, losses | ✅ validated | 1 | 8 |
| S32 | 2-D electrostatics, P1 FEM (capacitance from field energy) | ✅ validated | 2 | 0 |
| S33 | Biot-Savart integration of straight filament segments, loop and solenoid fields | ✅ validated | 3 | 0 |
| S34 | Mie series for dielectric and perfectly conducting spheres | ✅ validated | 2 | 0 |
| S35 | Fresnel coefficients and characteristic matrices of planar multilayers | ✅ validated | 2 | 0 |
| S36 | Jiles-Atherton hysteresis model (RK4 along an applied field path) | ✅ validated | 1 | 0 |
| S37 | Dispersive media (Drude, Lorentz, Debye) and their auxiliary-differential-equation coefficients | ✅ validated | 1 | 0 |
| S38 | Maxwell physics checks of predicted fields (Gauss, Faraday, Ampere-Maxwell, continuity, Poynting, interfaces, reciprocity, passivity) | ✅ validated | 4 | 2 |
| S39 | Density-based topology optimisation (SIMP, filter, projection, OC, MMA; compliance, thermal, Stokes-Brinkman, machine rotor) | ✅ validated | 1 | 2 |
| S40 | Yee FDTD in 1-D/2-D/3-D (CPML, Courant check, Drude/Lorentz/Debye ADE, PEC/PMC/periodic/Bloch, TF/SF plane waves, DFT monitors, sub-cell averaging) | ✅ validated | 4 | 6 |
| S41 | Near-to-far-field transform on a closed box (FDTD radiation patterns) | ✅ validated | 1 | 0 |
Training methods¶
| Id | Item | Status | Reference tests | Other tests |
|---|---|---|---|---|
| T1 | Base trainer: AMP, gradient accumulation, auto batch size, CUDA graphs, profiler | 🟡 tested, no reference | 0 | 9 |
| T2 | Distributed: DDP, FSDP, SLURM, torchrun, PowerSGD | ⚪ no test | 0 | 0 |
| T3 | Causal training | ⚪ no test | 0 | 0 |
| T4 | Time marching | ⚪ no test | 0 | 0 |
| T5 | Two phases Adam -> L-BFGS + L-BFGS finetune | 🟡 tested, no reference | 0 | 6 |
| T6 | Multi-restart | ⚪ no test | 0 | 0 |
| T7 | Adaptive residual-based collocation | ⚪ no test | 0 | 0 |
| T8 | Loss balancing: ReLoBRaLo, SoftAdapt, PCGrad, Augmented Lagrangian, Inverse Dirichlet, LR Annealing, AutoBalancer | ✅ validated | 1 | 6 |
| T9 | Weight schedulers: SA-PINN, GradNorm, LossRatio, NTK | 🟡 tested, no reference | 0 | 2 |
| T10 | Domain decomposition: XPINN, DoMINO/D3M | 🟡 tested, no reference | 0 | 2 |
| T11 | Inverse PINN (learnable physical parameters) | 🟡 tested, no reference | 0 | 3 |
| T12 | Gray-box + symbolic regression (PySR) | ⚪ no test | 0 | 0 |
| T13 | Uncertainty: heteroscedastic, B-PINN, MC Dropout, deep ensembles | 🟡 tested, no reference | 0 | 20 |
| T14 | SINDy | 🟡 tested, no reference | 0 | 2 |
| T15 | Adaptive hyperparameter sweep / architecture search (arena NAS) | ⚪ no test | 0 | 0 |
| T16 | Noether trainer (research only) | 🟡 tested, no reference | 0 | 1 |
| T17 | Post-training advisor / audit | ⚪ no test | 0 | 0 |
| T18 | Meta-learning: MAML, Reptile | 🟡 tested, no reference | 0 | 6 |
| T19 | Transfer learning (freeze, adapters, parametric) | 🟡 tested, no reference | 0 | 3 |
| T20 | Self-scaled quasi-Newton: BFGS / SSBFGS / SSBroyden (new, 2026-09-24) | ✅ validated | 1 | 3 |
| T21 | Autoresearch loop (fixed-budget trials, keep/revert, random or LLM proposer) | 🟡 tested, no reference | 0 | 2 |
| T22 | Large Physics Model blocks (Fourier encoding, multi-scale neighbourhoods, geometry code, ensemble UQ, OOD score, fine-tuning) | 🟡 tested, no reference | 0 | 1 |
Physical equations¶
| Id | Item | Status | Reference tests | Other tests |
|---|---|---|---|---|
| E1 | Laplace | ✅ validated | 7 | 28 |
| E2 | Poisson | ✅ validated | 15 | 24 |
| E3 | Helmholtz | ✅ validated | 2 | 1 |
| E4 | Heat (steady anisotropic / transient) | ✅ validated | 4 | 13 |
| E5 | Wave | ✅ validated | 1 | 0 |
| E6 | Advection-diffusion / convection | ✅ validated | 1 | 0 |
| E7 | Burgers (viscous / inviscid) | ✅ validated | 10 | 50 |
| E8 | Reaction-diffusion 1D/2D (Gray-Scott) | ✅ validated | 2 | 1 |
| E9 | Fisher-KPP | ✅ validated | 1 | 3 |
| E10 | Incompressible Navier-Stokes 2D/3D | 🟡 tested, no reference | 0 | 13 |
| E11 | Navier-Stokes in a rotating frame | 🟡 tested, no reference | 0 | 2 |
| E12 | Stokes | ✅ validated | 1 | 1 |
| E13 | Brinkman | ✅ validated | 1 | 0 |
| E14 | Darcy | 🟡 tested, no reference | 0 | 12 |
| E15 | Buckley-Leverett two-phase | ✅ validated | 1 | 0 |
| E16 | Compressible Euler 1D/2D/axisymmetric/rotating 3D | ✅ validated | 3 | 1 |
| E17 | Shallow water 1D/2D | ✅ validated | 1 | 6 |
| E18 | Stommel gyre | ✅ validated | 2 | 0 |
| E19 | Plane-stress / plane-strain linear elasticity | ✅ validated | 2 | 5 |
| E20 | Axisymmetric elasticity (+ torsion) / Lame | ✅ validated | 1 | 4 |
| E21 | Neo-Hookean hyperelasticity | ✅ validated | 1 | 0 |
| E22 | Euler-Bernoulli beam | ✅ validated | 1 | 11 |
| E23 | von Karman beam / plate | ✅ validated | 2 | 6 |
| E24 | Thermoelasticity | ✅ validated | 1 | 0 |
| E25 | Phase-field fracture | ⚪ no test | 0 | 0 |
| E26 | Biot poroelasticity | ✅ validated | 1 | 0 |
| E27 | Maxwell TE | ✅ validated | 1 | 0 |
| E28 | Bekker-Wong terramechanics | ✅ validated | 1 | 2 |
| E29 | Compressor meanline 1D | ✅ validated | 2 | 3 |
| E30 | Phonon Boltzmann transport 1D (gray) | ✅ validated | 3 | 1 |
| E31 | Black-Scholes | ✅ validated | 1 | 2 |
| E32 | Heston | ✅ validated | 2 | 1 |
| E33 | Opinion dynamics (continuum Hegselmann-Krause) | ✅ validated | 1 | 0 |
| E34 | Kepler two-body orbit | ✅ validated | 1 | 6 |
| E35 | Circular restricted three-body problem (planar, synodic) | ✅ validated | 3 | 3 |
| E36 | J2 perturbation | ✅ validated | 1 | 1 |
| E37 | Clohessy-Wiltshire relative motion | ✅ validated | 1 | 1 |
| E38 | Euler rigid-body attitude | ✅ validated | 1 | 1 |
| E39 | Lane-Emden polytrope | ✅ validated | 5 | 19 |
| E40 | Shakura-Sunyaev accretion disk | ✅ validated | 6 | 4 |
| E41 | Schwarzschild weak-field light bending | ✅ validated | 2 | 3 |
| E42 | SIR epidemic | ✅ validated | 1 | 0 |
| E43 | Pharmacokinetics two-compartment | ✅ validated | 1 | 0 |
| E44 | Reaction network / Arrhenius / mass action | 🟡 tested, no reference | 0 | 10 |
| E45 | Hagen-Poiseuille | 🟡 tested, no reference | 0 | 2 |
| E46 | Blasius friction factor | ✅ validated | 2 | 10 |
| E47 | Colebrook-White | 🟡 tested, no reference | 0 | 8 |
| E48 | Darcy-Weisbach pressure drop | ⚪ no test | 0 | 0 |
| E49 | Herschel-Bulkley + Metzner-Reed (non-Newtonian pipe flow) | 🟡 tested, no reference | 0 | 4 |
| E50 | DNV-RP-O501 erosion (straight pipe and bend) | ⚪ no test | 0 | 0 |
| E51 | Lame thick-walled cylinder | 🟡 tested, no reference | 0 | 3 |
| E52 | von Mises equivalent stress | 🟡 tested, no reference | 0 | 11 |
| E53 | Euler buckling + constrained rod buckling | ✅ validated | 1 | 6 |
| E54 | Beam-column moment amplification factor | 🟡 tested, no reference | 0 | 3 |
| E55 | S-N curve + Goodman + Miner | ✅ validated | 1 | 14 |
| E56 | Torsional stick-slip with Stribeck friction | 🟡 tested, no reference | 0 | 6 |
| E57 | Heat exchanger (effectiveness-NTU) | 🟡 tested, no reference | 0 | 8 |
| E58 | Fin array conduction | 🟡 tested, no reference | 0 | 4 |
| E59 | Control valve (Cv, compressible / incompressible) | 🟡 tested, no reference | 0 | 1 |
| E60 | Polytropic compression path | 🟡 tested, no reference | 0 | 1 |
| E61 | Real gas equation of state (CoolProp) | 🟡 tested, no reference | 0 | 2 |
| E62 | Compressor similarity map | ✅ validated | 2 | 0 |
| E63 | Helmholtz resonator | 🟡 tested, no reference | 0 | 4 |
| E64 | Membrane diffusion | 🟡 tested, no reference | 0 | 5 |
| E65 | Cantilever fatigue | ✅ validated | 1 | 4 |
| E66 | Electrostatics (Gauss's law with permittivity), differential and integral form | ✅ validated | 1 | 0 |
| E67 | Magnetostatics in the vector potential A_z | ✅ validated | 1 | 0 |
| E68 | Magneto-quasistatic eddy currents (time-harmonic A_z) | ✅ validated | 1 | 0 |
| E69 | Maxwell TMz time domain, differential and integral (Ampere-Maxwell circulation, Faraday) form | ✅ validated | 1 | 0 |
| E70 | Maxwell's curl equations in 3-D with optional Gauss constraints | ✅ validated | 1 | 0 |
| E71 | Frequency-domain TMz wave equation with complex permittivity | ✅ validated | 1 | 0 |
Physical problems¶
| Id | Item | Status | Reference tests | Other tests |
|---|---|---|---|---|
| P1.1 | Academic: burgers_1d | ✅ validated | 9 | 43 |
| P1.2 | Academic: channel_flow_3d | 🟡 tested, no reference | 0 | 4 |
| P1.3 | Academic: darcy_pressure_only_3d | ⚪ no test | 0 | 0 |
| P1.4 | Academic: helmholtz_acoustics_3d | ⚪ no test | 0 | 0 |
| P1.5 | Academic: laplace_2d | ✅ validated | 6 | 15 |
| P1.6 | Academic: lid_driven_cavity_3d | ⚪ no test | 0 | 0 |
| P1.7 | Academic: ns_incompressible_2d | 🟡 tested, no reference | 0 | 7 |
| P1.8 | Academic: pipe_flow_3d | ⚪ no test | 0 | 0 |
| P1.9 | Academic: poisson_2d | ✅ validated | 4 | 15 |
| P1.10 | Academic: reaction_diffusion_2d | ✅ validated | 2 | 1 |
| P1.11 | Academic: steady_heat_conduction_3d | 🟡 tested, no reference | 0 | 1 |
| P1.12 | Academic: transient_heat_3d | ⚪ no test | 0 | 0 |
| P1.13 | Academic: wave_ultrasound_3d | ⚪ no test | 0 | 0 |
| P2.1 | Solids: axisymmetric_linear_elasticity_2d | ⚪ no test | 0 | 0 |
| P2.2 | Solids: linear_elasticity_3d | 🟡 tested, no reference | 0 | 5 |
| P2.3 | Solids: linear_elasticity_3d_industry | 🟡 tested, no reference | 0 | 1 |
| P2.4 | Solids: material_fracture_2d | ⚪ no test | 0 | 0 |
| P2.5 | Solids: plane_strain_2d | ⚪ no test | 0 | 0 |
| P2.6 | Solids: plane_stress_2d | ✅ validated | 1 | 0 |
| P2.7 | Solids: rotary_coupling_torsion | ⚪ no test | 0 | 0 |
| P2.8 | Solids: thermoelasticity_2d | 🟡 tested, no reference | 1 | 0 |
| P2.9 | Solids: thick_walled_cylinder_lame | 🟡 tested, no reference | 0 | 1 |
| P2.10 | Solids: threaded_coupling_tc50_box | ⚪ no test | 0 | 0 |
| P2.11 | Solids: threaded_coupling_tc50_pin | ⚪ no test | 0 | 0 |
| P2.12 | Solids: threaded_coupling_tc50_rotating | ⚪ no test | 0 | 0 |
| P2.13 | Solids: von_mises_2d | ⚪ no test | 0 | 0 |
| P3.1 | Aero / automotive: aircraft_wing_aerodynamics | ⚪ no test | 0 | 0 |
| P3.2 | Aero / automotive: aircraft_wing_structural | ⚪ no test | 0 | 0 |
| P3.3 | Aero / automotive: car_brake_thermal | ✅ validated | 1 | 3 |
| P3.4 | Aero / automotive: car_external_aero | ⚪ no test | 0 | 0 |
| P3.5 | Aero / automotive: car_suspension_fatigue | ⚪ no test | 0 | 0 |
| P3.6 | Aero / automotive: rocket_nozzle_cfd | ⚪ no test | 0 | 0 |
| P3.7 | Aero / automotive: rocket_structural | ⚪ no test | 0 | 0 |
| P4.1 | Turbomachinery: axial_compressor_cascade_2d | ⚪ no test | 0 | 0 |
| P4.2 | Turbomachinery: axial_compressor_meanline | ✅ validated | 1 | 2 |
| P4.3 | Turbomachinery: axial_compressor_stage_3d | ✅ validated | 1 | 0 |
| P4.4 | Turbomachinery: fan_cooler_cfd | 🟡 tested, no reference | 0 | 1 |
| P5.1 | Industrial thermal: cpu_heatsink_thermal | ✅ validated | 2 | 6 |
| P5.2 | Industrial thermal: datacenter_airflow_2d | ⚪ no test | 0 | 0 |
| P5.3 | Industrial thermal: datacenter_cfd_3d | ⚪ no test | 0 | 0 |
| P5.4 | Industrial thermal: datacenter_server_thermal | ✅ validated | 1 | 0 |
| P5.5 | Industrial thermal: furnace_combustion_zone | ⚪ no test | 0 | 0 |
| P5.6 | Industrial thermal: industrial_furnace_thermal | ✅ validated | 1 | 2 |
| P5.7 | Industrial thermal: pcb_thermal | ✅ validated | 1 | 5 |
| P5.8 | Industrial thermal: refractory_lining | ✅ validated | 1 | 0 |
| P6.1 | Multidisciplinary: black_scholes_1d | ✅ validated | 1 | 2 |
| P6.2 | Multidisciplinary: climate_atmosphere_2d | ⚪ no test | 0 | 0 |
| P6.3 | Multidisciplinary: climate_ocean_gyre | ⚪ no test | 0 | 0 |
| P6.4 | Multidisciplinary: crystal_phonon | ✅ validated | 1 | 0 |
| P6.5 | Multidisciplinary: drug_diffusion_tissue | ⚪ no test | 0 | 0 |
| P6.6 | Multidisciplinary: heston_pde_2d | 🟡 tested, no reference | 2 | 1 |
| P6.7 | Multidisciplinary: opinion_dynamics_2d | ✅ validated | 1 | 0 |
| P6.8 | Multidisciplinary: pk_two_compartment | ✅ validated | 1 | 0 |
| P6.9 | Multidisciplinary: sir_epidemic | ⚪ no test | 0 | 0 |
| P7.1 | Astro / space: cr3bp_planar_synodic | ✅ validated | 3 | 2 |
| P7.2 | Astro / space: kepler_two_body_orbit | ✅ validated | 1 | 2 |
| P7.3 | Astro / space: lane_emden_polytrope | ✅ validated | 2 | 8 |
| P7.4 | Astro / space: nfw_dark_matter_potential | ✅ validated | 1 | 1 |
| P7.5 | Astro / space: satellite_j2_perturbation | ✅ validated | 1 | 1 |
| P7.6 | Astro / space: schwarzschild_light_bending_weak_field | ✅ validated | 1 | 2 |
| P7.7 | Astro / space: shakura_sunyaev_accretion_disk | ✅ validated | 1 | 3 |
| P7.8 | Astro / space: sod_shock_tube_astro | ⚪ no test | 0 | 0 |
| P7.9 | Astro / space: space_debris_cw_relative_motion | ✅ validated | 1 | 1 |
| P7.10 | Astro / space: spacecraft_attitude_euler_rotation | ✅ validated | 1 | 1 |
| P8.1 | Terramechanics: bekker_wong_surrogate_2d | ✅ validated | 1 | 2 |
| P9 | PINNeAPPle-CFD v1: pipes + particle erosion (CFD-04 pilot) | ⚪ no test | 0 | 0 |