Model atlas

NAVIER-CFD registers 55 reviewed neural-numerical methods in a uniform executable catalog. The catalogue covers:

• Physics-informed: PINN, NSFnets, PINNsFormer, PINO, PI-MFM, RiemannONet.
• Deep operator learning: DeepONet, MIONet, Fourier-DeepONet, Nested Fourier-DeepONet, Fourier-MIONet.
• Spectral operators: FNO, F-FNO, U-FNO, U-NO, LSM, MWT, Laplace NO, state-space NO.
• Geometry and transformers: Geo-FNO, GINO, GNOT, Galerkin Transformer, FactFormer, ONO, Transolver, UPT, MeshGraphNets, DoMINO, ReViT.
• CFD-specialized models: PIBERT, FourierFlow, P3D, AeroTransformer, NeuralDEM, DeepM&Mnet, Energy Transformer.
• Foundation and generative models: DPOT, Poseidon, PROSE-FD, BCAT, PDEformer-1, Tadpole, PDE-Refiner, FunDiff, Flow Matching for PDEs.
• Acceleration frameworks: Solver-in-the-Loop, INC, PICT, diffSPH, NeuroSEM, neural-operator preconditioned Newton, geometry-aware neural preconditioning.
• Uncertainty and time adaptation: Conformalized-DeepONet and TANTE.

Use navier models list and navier models info <id> for the current machine-readable card.

Visual architecture cards

The following detailed cards include two diagrams:

1. Method architecture — a concise conceptual flow of the scientific method.
2. NAVIER-CFD library flow — how canonical data, dataset-conditioned construction, the model hub, training, diagnostics, and FigureLab connect around that model.

Model card	Scientific role	Registry ID
PIBERT	Multiscale physics-informed CFD transformer	pibert
GINO	Geometry-informed neural operator	gino
Transolver	Physics-attention transformer for general geometries	transolver
UPT	Representation-flexible latent physics transformer	upt
P3D	High-resolution three-dimensional surrogate	p3d
AeroTransformer	Pretrained three-dimensional aerodynamic transformer	aerotransformer
DoMINO	Decomposable multiscale point-cloud operator	domino
FourierFlow	Frequency-guided generative flow prediction	fourierflow
INC	Equation-level neural corrector	inc
PICT	Differentiable multi-block PISO solver	pict
Geometry-aware preconditioner	Learned preconditioning inside an iterative solver	geometry_preconditioner

Diagram conventions

flowchart LR
    X["Scientific inputs"] --> M["Model-specific method"] --> Y["Physical outputs"]
    D["Dataset provider"] --> A["Canonical adapter"] --> S["CFDSample / CFDBatch"]
    S --> C["Dataset-conditioned configuration"] --> H["ModelHub"]
    H --> T["Training / execution"] --> V["Metrics and diagnostics"] --> F["FigureLab and manifests"]

    classDef science fill:#e9f8fb,stroke:#167d9a,stroke-width:1.5px,color:#17324d;
    classDef output fill:#eef8f0,stroke:#34855c,stroke-width:1.5px,color:#173f2b;
    classDef verify fill:#fff4e8,stroke:#c97932,stroke-width:1.5px,color:#5a3518;
    class X,M,D,A,S,C,H,T science;
    class Y output;
    class V,F verify;

The method diagram is an explanatory summary, not automatically a claim of exact reproduction. NAVIER-CFD native reference implementations are executable integration models; a paper-level reproduction requires the original architecture, preprocessing, checkpoints, and benchmark settings to be pinned and reported.

Common executable path

from navier_cfd import load_model

model, build_plan = load_model(
    "transolver",
    dataset="airfrans",
    sample=sample,
    return_plan=True,
)

Configuration resolution follows:

explicit constructor arguments
            ↑
user overrides
            ↑
actual CFDSample shape and metadata
            ↑
registered dataset defaults

The remaining registered methods are available through the machine-readable catalog and will receive detailed visual cards as their model-specific documentation is expanded.