OneScience-Group/RNO

RNO

Model Introduction

RNO (Radon Neural Operator), proposed by researchers from Zhejiang University of Technology, learns PDE solution mappings with both global and local features in the sinogram domain through the Radon transform.

This repository is an independent OneScience reproduction of the Darcy-flow experiment. RNO learns the parameterized Darcy solution operator and predicts steady pressure from a porous-medium permeability or diffusion-coefficient field.

Paper: Solving Partial Differential Equations via Radon Neural Operator

Model Description

For Darcy flow, RNO maps a two-dimensional permeability or diffusion-coefficient field (a(x,y)) to its scalar pressure solution (u(x,y)).

The architecture consists of feature lifting, Physics-Attention, a Radon block, and output projection. The input field and spatial coordinates are lifted to high-dimensional features; Physics-Attention extracts nonlocal information; and the Radon block projects features into the sinogram domain. Angle reweighting and sinogram convolution learn the contribution of different projection directions before filtered back-projection restores spatial features for the final Darcy solution.

Intended Uses

Use case	Description
Darcy-flow prediction	Predict steady porous-medium pressure from a two-dimensional permeability or diffusion field.
Parameterized PDE solution	Learn an operator from coefficients, initial conditions, or boundary conditions to PDE solutions.
Scientific surrogate	Replace part of a costly numerical solve with fast batched prediction.
Cross-resolution prediction	Evaluate the learned operator at different spatial resolutions when supported by the training setup.

Usage

1. OneCode

Launch the OneCode AI-for-Science environment

2. Manual Setup

Hardware requirements

• A GPU or DCU is recommended.
• A CPU can run imports and small connectivity checks, but full training and inference will be slow.
• DCU users should install DTK 25.04.2 or later, or the OneScience-recommended version for the cluster.

Download the model repository from Hugging Face

pip install -U huggingface_hub
hf download OneScience-Group/RNO --local-dir ./RNO
cd RNO

Install the runtime environment

DCU environment

# Activate DTK first.
conda create -n onescience311 python=3.11 -y
conda activate onescience311
pip install onescience[cfd-dcu] -i http://mirrors.onescience.ai:3141/pypi/simple/ --trusted-host mirrors.onescience.ai

GPU environment

conda create -n onescience311 python=3.11 -y libstdcxx-ng=12 libgcc-ng=12 gcc_linux-64=12 gxx_linux-64=12
conda activate onescience311
pip install onescience[cfd-gpu] -i http://mirrors.onescience.ai:3141/pypi/simple/ --trusted-host mirrors.onescience.ai

Download the training dataset from Hugging Face

hf download OneScience-Group/cfd_benchmark \
  --repo-type dataset \
  --local-dir ./data

The Darcy files are stored under data/data/darcy/ after this download:

data/data/darcy/
├── piececonst_r421_N1024_smooth1.mat
└── piececonst_r421_N1024_smooth2.mat

Set data.root in config/config.yaml to the Darcy directory. Each MAT file contains 1,024 regular-grid samples at the original 421 x 421 resolution:

• coeff: the Darcy permeability or diffusion-coefficient field.
• sol: the corresponding steady pressure solution.

This experiment uses piececonst_r421_N1024_smooth1.mat for training and piececonst_r421_N1024_smooth2.mat for testing, with downsampling and normalization defined by the experiment configuration.

Train

python scripts/train.py --config config/config.yaml

Per-epoch metrics are logged and printed at the configured interval. The checkpoint with the lowest training relative L2 is saved to weight/best_model.pth.

Pretrained weights

The repository includes a Darcy-trained RNO checkpoint at weight/best_model.pth for inference or continued training.

Inference and evaluation

python scripts/inference.py \
  --config config/config.yaml \
  --checkpoint weight/best_model.pth \
  --device auto

The script evaluates the fixed test set, prints the mean per-sample relative L2, computes relative L2 and gradient-relative L2 against paper references, and writes:

results/evaluation_metrics.json
results/predictions.npz

predictions.npz contains predicted and target pressure fields, normalized permeability fields, and per-sample relative L2 values.

Visualization

python scripts/result.py --results results

Outputs:

results/training_curve.png
results/darcy_prediction.png
results/visualization_summary.json

• training_curve.png shows total training loss, relative L2, and gradient-relative L2.
• darcy_prediction.png compares permeability, target pressure, predicted pressure, and absolute error.
• visualization_summary.json records visualization paths, test relative L2, and the paper comparison.

OneScience

Platform	OneScience repository	OneSkills repository
Gitee	https://gitee.com/onescience-ai/onescience	https://gitee.com/onescience-ai/oneskills
GitHub	https://github.com/onescience-ai/OneScience	https://github.com/onescience-ai/oneskills

Citation and License

• Paper: Solving Partial Differential Equations via Radon Neural Operator.
• Official implementation: wenbin-lu/Radon-Neural-Operator, released under the MIT License.
• This repository uses the Hugging Face-compatible MIT identifier (mit). The dataset and other third-party resources remain subject to their original licenses and terms.