NAVIER-CFD

Neural and Agentic Verification, Integration, Evaluation, and Recommendation for Computational Fluid Dynamics

NAVIER-CFD is a CFD-first Python platform for importing, configuring, training, testing, comparing, and recommending neural PDE/CFD models across heterogeneous datasets.

multi-dataset integration
+ multi-family model hub
+ dataset-conditioned construction
+ unified training and checkpoints
+ physical metric suites
+ evidence-aware recommendation
+ Codex-integrated AutoResearch
+ chemical-engineering extensions

Version 1.1.0 adds NAVIER AutoResearch: persistent research contracts, bounded agent sessions, Codex repository skills, a local read-only MCP server, deterministic CFD diagnostics, and auditable research-grade figure specifications.

Authors and affiliation

Somyajit Chakraborty¹, Kaiyuan Yang¹, Xizhong Chen¹*

¹State Key Laboratory of Synergistic Chem-Bio Synthesis, Department of Chemical Engineering,
School of Chemistry and Chemical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China

Correspondence

• Xizhong Chen（陈锡忠）: chenxizh@sjtu.edu.cn
• Somyajit Chakraborty（叶一明）: chksomyajit@sjtu.edu.cn

* Corresponding author.

Install

pip install "navier-cfd[models]"

Official The Well provider support:

pip install "navier-cfd[models,the-well]"

Codex, MCP, and research-figure support:

pip install "navier-cfd[autoresearch]"

Core catalog, recommendation, evidence, dataset-discovery, and NumPy metric tools:

pip install navier-cfd

NAVIER AutoResearch and Codex

Start an approval-aware campaign from a client problem:

navier-autoresearch init \
  "Reconstruct gas and solids velocities from EP_G history across unseen gas velocities" \
  --workspace runs/bubblenet-autoresearch \
  --domain gas_solid_multiphase \
  --mode guided \
  --max-gpu-hours 24 \
  --max-experiments 12

The campaign records a research contract, deterministic planner output, action proposals, approvals, findings, resource usage, and stopping decisions.

Codex integration is provided through:

• a repository AGENTS.md with scientific-integrity and autonomy rules;
• six skills under .agents/skills;
• a project MCP example under .codex/config.toml.example;
• the local navier-autoresearch mcp STDIO server.

The v1.1.0 MCP tools are intentionally read-only: dataset/model discovery, research planning, recommendation, metric catalog inspection, and figure-spec auditing. Training, solvers, cluster submission, large downloads, overwrites, and deletion are not exposed as automatic tools.

from navier_cfd import AutoResearchSession, ResearchBudget, ResearchMode

session = AutoResearchSession.create(
    "runs/client-project",
    "Predict pressure drop and temperature fields for unseen heat-exchanger geometries",
    domain="heat_transfer",
    mode=ResearchMode.GUIDED,
    budget=ResearchBudget(max_gpu_hours=20, max_experiments=10),
)
plan = session.plan()

Detailed documentation:

• AutoResearch overview
• AutoResearch architecture
• MCP tools
• Codex skills
• Research contracts and sessions
• CFD diagnostics
• FigureLab

Dataset-conditioned model construction

from navier_cfd import load_model

fno = load_model("fno", dataset="cfdbench")
p3d = load_model("p3d", dataset="scalarflow")
transolver = load_model("transolver", dataset="airfrans")
gino = load_model("gino", dataset="drivaerml")

An actual canonical sample overrides static assumptions about dimensionality, coordinates, channels, history length, and sensor count:

model, plan = load_model(
    "pibert",
    dataset="realpdebench",
    sample=sample,
    overrides={"hidden_dim": 256, "num_layers": 8, "num_heads": 8},
    return_plan=True,
)

print(plan.to_dict())

Resolution priority:

explicit model keyword arguments
              ↑
user overrides
              ↑
actual CFDSample shapes
              ↑
registered dataset defaults

Registered dataset families

Dataset	Representation	Dimension	Primary use
PDEBench	Structured	1D–3D	PDE forecasting and operator learning
CFDBench	Structured	2D	Cavity, tube, dam and cylinder CFD
RealPDEBench	Structured	2D	Simulation-to-real forecasting
The Well	Structured provider family	2D/3D	Multiphysics fields and pretraining
APEBench	Structured	1D–3D	Autoregressive PDE emulation
ScalarFlow	Structured	3D	Volumetric scalar transport
AirfRANS	Point cloud/unstructured	2D	RANS airfoil geometry
DrivAerNet++	Point cloud/unstructured	3D	Vehicle aerodynamics
DrivAerML	Unstructured	3D	High-fidelity vehicle CFD
ShapeNet-Car	Point cloud	3D	Geometry-conditioned vehicle fields
EAGLE	Structured/unstructured	2D/3D	Fluid and geometry learning

Official The Well provider

The Well is not treated as one fictitious datasets.load_dataset("polymathic-ai/the_well") repository. NAVIER-CFD calls its official the_well.data.WellDataset backend with:

hf://datasets/polymathic-ai/
+ individual well_dataset_name

Load one configuration:

from navier_cfd import load_cfd_dataset, load_model

dataset = load_cfd_dataset(
    "the_well",
    configuration="active_matter",
    split="train",
    streaming=True,
    n_steps_input=4,
    n_steps_output=1,
    use_normalization=True,
)

sample = dataset[0]
model = load_model("fno", dataset="the_well", sample=sample)

The adapter preserves:

• variable and constant field semantics;
• input and output time grids;
• spatial coordinates;
• scalar parameters;
• boundary-condition metadata;
• normalization type and statistics provenance;
• provider version and access plan;
• official train, valid, and test split identity.

Time history is flattened into channels by default, allowing the model builder to infer the physical spatial dimension and correct input/output widths.

Native reference model coverage

NAVIER-CFD provides 52 executable reference implementations across:

• operator learning: DeepONet, MIONet, FNO/PINO, Geo-FNO, GINO, U-FNO, F-FNO, U-NO, LSM, GNOT, Galerkin Transformer, MWT, FactFormer, ONO, Transolver, Laplace NO, and State-Space NO;
• physics-informed ML: PINN, NSFnets, PINNsFormer, PIBERT, PI-MFM, RiemannONet, and DeepM&Mnet;
• geometry and foundation models: MeshGraphNets, DoMINO, UPT, DPOT, Poseidon, PROSE-FD, BCAT, PDEformer-1, P3D, AeroTransformer, Tadpole, and ReViT;
• generative, correction, preconditioning, adaptation, and uncertainty: FourierFlow, PDE-Refiner, solver-in-the-loop, INC, NeuroSEM, neural preconditioners, conformal prediction, TANTE-style adaptation, Energy Transformer, FunDiff, and flow matching.

PICT, diffSPH, and NeuralDEM remain specialized external integrations because meaningful execution requires their dedicated CFD or particle runtimes.

A NAVIER-CFD native reference implementation is executable, trainable, checkpointable, and forward/backward tested. It is not automatically a bit-for-bit reproduction of every author repository, unpublished preprocessing pipeline, private checkpoint, or paper table.

Canonical dataset layer

from navier_cfd import AdaptedDataset, AdapterRegistry, make_dataloaders

adapter = AdapterRegistry().adapter(
    "airfrans",
    input_key="node_features",
    target_key="fields",
    coordinate_key="pos",
    target_fields=("pressure", "velocity_x", "velocity_y"),
)

dataset = AdaptedDataset(raw_airfrans, adapter)
loaders = make_dataloaders(dataset, batch_size=4, seed=42)

CFDSample and CFDBatch support structured fields, point clouds, mesh nodes, variable-size samples, padding, masks, coordinates, physical parameters, and metadata.

Unified training and evaluation

from navier_cfd import CFDTrainer, MetricContext, TrainerConfig

metric_context = MetricContext(
    sample_axis=0,
    spatial_axes=(1, 2),
    channel_axis=-1,
    velocity_channels=(0, 1),
    spacing=(dx, dy),
)

trainer = CFDTrainer(
    model,
    model_id="transolver",
    config=TrainerConfig(
        epochs=200,
        optimizer="adamw",
        learning_rate=1e-3,
        mixed_precision=True,
        checkpoint_dir="runs/checkpoints",
        early_stopping_patience=20,
    ),
)

training = trainer.fit(loaders["train"], loaders["validation"])
metrics = trainer.evaluate(
    loaders["test"],
    metric_suites=("data_standard", "fluid_standard"),
    metric_context=metric_context,
)

The common trainer supports Adam, AdamW, SGD, LBFGS, mixed precision, gradient clipping, cosine and plateau schedulers, early stopping, periodic checkpoints, and custom forward/loss functions.

Metric suites

from navier_cfd import MetricContext, MetricSuite

context = MetricContext(
    sample_axis=0,
    time_axis=1,
    spatial_axes=(2, 3),
    channel_axis=-1,
    velocity_channels=(0, 1),
    spacing=(dx, dy),
    profile_axis=2,
)

suite = MetricSuite.combine([
    "data_standard",
    "the_well",
    "realpdebench",
    "fluid_standard",
])
results = suite.evaluate(prediction, target, context=context)

Suite	Metrics
data_standard	MSE, RMSE, MAE, L∞, relative L1/L2, NMSE, NRMSE, R², Pearson, cosine
the_well	The Well-style normalized errors, VMSE, VRMSE, and binned spectral MSE
realpdebench	RMSE, MAE, per-sample relative L2, R², fRMSE, frequency error, turbulent KE, MVPE, Update Ratio
fluid_standard	RMSE, relative L2, spectral, divergence, kinetic-energy, and vorticity errors

Every result records its category, optimization direction, ideal value, assumptions, validity, and evaluation space. Missing physical metadata returns valid=False with an explanation rather than a fabricated quantity.

Research-grade figures and diagnostics

from navier_cfd import FigureSpec, audit_figure_spec, analyze_interface_error

spec = FigureSpec(
    figure_type="truth_prediction_error",
    fields=("gas_velocity_y",),
    units="m/s",
    shared_color_limits=True,
    error_definition="absolute",
    mask="fluid_cells",
)
assert audit_figure_spec(spec).valid

interface_report = analyze_interface_error(
    prediction,
    target,
    gas_volume_fraction,
    spatial_axes=(1, 2),
)

The figure audit detects misleading color scales, missing units, undeclared masks, normalized fields mislabeled as physical quantities, visual smoothing, cherry-picking, low raster resolution, and missing vector output. Optional renderers create truth/prediction/error and profile figures with a FigureManifest sidecar.

High-level experiment API

from navier_cfd import Experiment, MetricContext, TaskSpec, TrainerConfig

experiment = Experiment(
    dataset_id="the_well",
    dataset_configuration="rayleigh_benard",
    model_id="pino",
    task=TaskSpec(
        problem="rayleigh_benard",
        task_type="forecasting",
        dimension=2,
        mesh_type="structured",
        temporal_mode="autoregressive",
        geometry_mode="fixed",
        physics=("incompressible_navier_stokes", "heat_transfer"),
    ),
    trainer_config=TrainerConfig(epochs=100, optimizer="adamw", mixed_precision=True),
    metric_suites=("data_standard", "the_well", "fluid_standard"),
    metric_context=MetricContext(velocity_channels=(0, 1), time_axis=1),
    output_dir="runs/pino-the-well",
)

# Preserve provider-native trajectories and avoid re-splitting overlapping windows.
splits = experiment.load_official_splits(streaming=True)
result = experiment.run(splits)

The experiment manifest records the provider, dataset configuration, split policy, model build plan, trainer configuration, checkpoints, metric definitions, context, assumptions, and results.

provider or raw dataset
   ↓
canonical adapter + field semantics
   ↓
dataset-aware model construction
   ↓
common trainer and checkpoints
   ↓
physical metric suites
   ↓
auditable experiment manifest

Evidence-aware recommendation

navier recommend \
  --problem vehicle_drag \
  --task surrogate \
  --dimension 3 \
  --mesh point_cloud \
  --temporal steady \
  --geometry varying \
  --physics aerodynamics \
  --fidelity rans \
  --memory-gb 80

The recommender combines architecture compatibility with task-matched paper evidence, evidence quality, metric comparability, Bayesian shrinkage, confidence, and coverage reporting.

Validation

pytest tests/test_model_hub.py tests/test_pibert_pipeline.py tests/test_native_suite.py
pytest tests/test_the_well_provider.py tests/test_metric_suites.py
pytest tests/test_autoresearch.py tests/test_autoresearch_tools.py tests/test_figurelab.py
node --test website/recommender/recommender-core.test.mjs
mkdocs build --strict

CI verifies Python 3.10–3.12, all 52 native reference models, official provider contracts, dataset-conditioned model construction, metric analytical cases, AutoResearch contracts and tools, FigureLab audits, the browser recommender, and bilingual documentation.

Documentation

• Project website: https://samsomyajit.github.io/NAVIER-CFD/
• Interactive recommender: https://samsomyajit.github.io/NAVIER-CFD/recommender/
• English documentation: https://samsomyajit.github.io/NAVIER-CFD/docs/
• Simplified Chinese documentation: https://samsomyajit.github.io/NAVIER-CFD/docs/zh/
• AutoResearch: docs/AUTORESEARCH.md
• Metrics: docs/METRICS.md
• The Well provider: docs/datasets/the_well.md
• Native model suite: docs/NATIVE_MODEL_SUITE.md

Citation and scientific scope

When publishing results, cite NAVIER-CFD for the integration workflow, the original model paper, the original dataset/benchmark paper, and the official upstream implementation/checkpoint where applicable.

The Well datasets, RealPDEBench, model papers, repositories, checkpoints, and numerical solvers retain their own licenses and citation requirements.

License

NAVIER-CFD is licensed under Apache-2.0.