DD-RNO: Domain-Decomposed Routed Neural Operator for Airfoil Flow Prediction

Official open-source implementation for DD-RNO (Domain-Decomposed Routed Neural Operator), a physics-guided deep learning surrogate for high-fidelity RANS flow field prediction ($u_x, u_y, p, \nu_t$) and direct surface force integration ($C_L, C_D$) around arbitrary airfoil profiles.

Key Features • Benchmark Results • Architecture • Getting Started • Citation & Credits

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Key Features

• Physics-Guided Domain Routing: Dynamically partitions the flow field into specialized regional decoders (Inviscid, Boundary Layer, Wake) routed via Reynolds-adaptive turbulent scaling ($\delta_{\text{BL}} \propto \text{Re}^{-1/5}$).
• Learned Canonical Quadrature (LCQ): Replaces error-prone numerical summation with a flow-conditioned inner product, implicitly recovering total aerodynamic force ($C_L, C_D$) and viscous drag signals directly from continuous surface pressure fields.
• Continuous SDF Geometry Trunk: Combines a 2D Fourier Neural Operator (FNO) grid encoder with Latent Grid Interpolation (LGI) and Multi-Scale Fourier Features to resolve steep near-wall shear layers at sub-grid precision.
• Instantaneous Mesh-Free Inference: Evaluates complete flow fields and aerodynamic forces directly from raw .dat boundary files in < 5 ms (~$10,000\times$ faster than standard OpenFOAM RANS solvers).

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Benchmark Results

Evaluated on the standardized AirfRANS benchmark dataset ($N_{\text{train}}=800$, $N_{\text{test}}=200$ across 1,000 steady-state RANS simulations):

Metric / Task	Baseline MLP	GraphSAGE	Graph U-Net	DD-RNO (Ours)	Improvement
Velocity $u_x$ MSE ($\times 10^{-2}$)	$1.58$	$1.72$	$1.68$	$0.091$	$17.4\times$ Lower Error
Reynolds OOD $u_x$ MSE ($\times 10^{-2}$)	$10.20$	$10.80$	$10.50$	$0.448$	$22.8\times$ Lower Error
Drag $C_D$ Relative Error (%)	$6.18%$	$7.37%$	$13.32%$	$1.09%$	$5.7\times$ Error Reduction
Drag Rank Correlation ($\rho_D$)	$0.250$	$0.194$	$0.092$	$0.997$	Near-Perfect ($\rho \to 1.0$)
Inference Speed	~10 min/sim	~5 min/sim	~5 min/sim	< 5 ms	$10,000\times$ Speedup

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Architecture

The end-to-end DD-RNO architecture maps Signed Distance Fields (SDF) and flow conditions $(\alpha, \text{Re})$ into continuous volumetric flow fields and integrated force coefficients ($C_L, C_D$):

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Getting Started

1. Installation

Clone the repository and install dependencies in a Python 3.10+ environment:

git clone https://github.com/taksh2406/DD-RNO.git
cd DD-RNO
pip install -r requirements.txt

2. Quickstart Inference

Predict aerodynamic coefficients and flow fields directly from a raw .dat file:

python example_inference.py

3. Python API Usage

from inference.predict import DDRNOPredictor

# Initialize predictor with pre-trained checkpoint and config
predictor = DDRNOPredictor("checkpoints/ddrno/best_cl.pt", "configs/ddrno.yaml")

# Predict Cl and Cd directly from a .dat airfoil file (NACA 0012 at alpha = 5 deg, Re = 3M)
result = predictor.predict_from_dat("naca0012.dat", aoa_deg=5.0, re=3e6)
print(f"Cl = {result['Cl']:.4f}, Cd = {result['Cd']:.5f}")
# Output: Cl = 0.4933, Cd = 0.01030

# Query continuous flow fields (ux, uy, p, nut) at arbitrary physical coordinates (x, y)
import numpy as np
query_points = np.array([[0.5, 0.1], [0.5, 0.0], [1.2, 0.0]])
res = predictor.predict_from_dat("naca0012.dat", aoa_deg=5.0, re=3e6, query_pts=query_points, return_field=True)
print("Flow fields shape:", res['field'].shape)  # (3, 4) -> [ux, uy, p, nut]

4. Training & Evaluation

To train DD-RNO from scratch on the Full task split:

python training/main_train.py --config configs/ddrno.yaml --seed 42

To evaluate a trained model checkpoint on the test split:

python evaluation/eval_full_mesh.py --ckpt checkpoints/ddrno/best_cl.pt --config configs/ddrno.yaml --split test

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Citation & Credits

If you use this work or codebase in your research, please credit:

T.A. Mehta, P.S. Bhati, and H.D. Akolekar, "DD-RNO: A Domain-Decomposed Routed Neural Operator for Airfoil Flow Prediction".
Paper Link: https://arxiv.org/abs/2608.13490

@article{mehta2026ddrno,
  title={DD-RNO: A Domain-Decomposed Routed Neural Operator for Airfoil Flow Prediction},
  author={Mehta, T. A. and Bhati, P. S. and Akolekar, H. D.},
  journal={arXiv preprint arXiv:2608.13490},
  year={2026},
  url={https://arxiv.org/abs/2608.13490}
}

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License

This project is open-source and licensed under the MIT License.