Physics-Informed Neural Network (PINN) CFD Simulation and Validation — NACA0012 Airfoil

This project demonstrates how to use a Physics-Informed Neural Network (PINN) to simulate compressible, viscous Navier–Stokes flow over a NACA0012 airfoil at Mach ≈ 1.2.

It integrates NVIDIA PhysicsNeMo and cüstomaised PyTorch-based fallback and an Validation that automatically checks mass conservation, boundary conditions, and lift/drag accuracy.

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🚀 Overview

The repo contains workflow for:

1. Generating the NACA0012 geometry and simulation grid.
2. Defining and training a Physics-Based model to solve the compressible Navier–Stokes equations.
3. Using PhysicsNeMo (if installed) for PDE residual computation.
4. Running an integrated Validator Agent every 100 epochs:
   • Checks mass conservation.
   • Enforces no-penetration boundary condition.
   • Computes Lift, Drag, Cl, and Cd.
   • Produces a PDF Proof of Simulation Report.

Each validation step also saves model checkpoints and plots streamlines and Cp contours. This automates the verification steps that are costly or subjective by computing the PDE residuals and check physics consistency, compare AI outputs to trusted solvers or learned surrogates, spot anomalies, outliers, or boundary-condition violations. In the end produce human-readable verdicts and evidence for on-chain contracts.

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🧠 PhysicsNeMo Integration

• If physicsnemo is installed, the notebook uses:

  from physicsnemo.sym.eq.pdes import navier_stokes as pn_ns
  ns_helper = pn_ns.NavierStokes(viscosity=1e-5, gamma=1.4)
  res = ns_helper.compute_residuals(xy, rho, u, v, p)

• If not available, it automatically falls back to a PyTorch autodiff-based Navier–Stokes residual evaluator.

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🧩 Runtime Environment

Recommended: Google Colab (GPU runtime)

1. Open the notebook in Google Colab.
2. Go to Runtime → Change runtime type → GPU.
3. Run all cells top-to-bottom.

Dependencies are installed automatically inside Colab:

!pip install numpy matplotlib scipy torch
# Optional (if you have NVIDIA PhysicsNeMo access)
!pip install physicsnemo

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⚙️ Training Configuration

Parameter	Description	Default
Epochs	Total training iterations	1000
Validator interval	How often the validator runs	every 100 epochs
Grid size	(nx, ny) = (300, 150)	adjustable
Network	4-layer MLP, 256 neurons, Tanh activations	fixed
Flow regime	Compressible (Mach ~ 1.2)	steady 2D
PDE	Navier–Stokes (energy equation included)

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📊 Validation Metrics

The Validator computes and logs the following:

Metric	Description
mass_div_mean	Mean absolute mass continuity residual
bc_no_pen_mean	RMS normal velocity at surface (no-penetration)
bc_no_pen_max	Maximum violation of BC
Lift, Drag	Integrated surface pressure forces
Cl, Cd	Normalized aerodynamic coefficients

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📑 Output Files

File	Description
validation_report_epoch_100.pdf	PDF “Proof of Simulation” report
ckpts/ckpt_epoch_100.pth	Model checkpoint
validation_report_epoch_200.pdf, etc.	Reports at subsequent validation steps

The PDF includes:

• Simulation metrics and metadata (timestamp, environment, torch version)
• Streamline plots over the airfoil
• Pressure coefficient contour (Cp)
• Numerical summary of validation results

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📘 Proof of Simulation Report Example

Contains

• Metadata (date/time, library versions)
• Metrics table (mass residuals, Cl/Cd)
• Plots:
  • Streamlines
  • Cp contour map

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🧪 Extending This Project

You can extend or modify this notebook to:

• Use other NACA airfoils (e.g., NACA 2412 or 4415)
• Add viscous wall models or turbulence closures
• Export ONNX models for real-time surrogate inference
• Add uncertainty quantification (UQ) or autoencoder-based anomaly detection
• Connect to NVIDIA PhysicsNemo or Omniverse

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🔐 Validation Provenance (Optional AI Proof)

Each PDF is timestamped and includes environment hashes. Extensions can be:

• Add SHA256 model checkpoints
• Include blockchain-style hash signatures for auditability
• Store validation reports in Google Drive automatically

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🏁 Citation

please cite:

NVIDIA PhysicsNeMo: Physics-Informed Neural Models for Simulation and Inference (2024)
https://developer.nvidia.com/physicsnemo

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🧭 License

MIT This repository is open for research and educational use.
© 2025