BENO
Model Overview
BENO is a boundary-embedded neural operator developed by researchers at Peking University for solving elliptic PDEs subject to complex boundary conditions. It enables rapid prediction of steady-state physical fields across varying geometries and nonhomogeneous boundary conditions.
Paper: BENO: Boundary-embedded Neural Operators for Elliptic PDEs
Model Description
BENO employs a boundary-embedded neural operator architecture that combines a dual-branch graph neural network with a Transformer. Trained on the BENO dataset, it predicts steady-state physical fields governed by elliptic PDEs such as the Poisson and Laplace equations on complex geometries with nonhomogeneous boundary conditions.
Use Cases
| Use Case | Description |
|---|---|
| Elliptic PDE solving | Rapidly approximate steady-state boundary-value problems such as the Poisson and Laplace equations |
| Complex boundary modeling | Capture the effects of free-form boundaries, irregular domains, and nonhomogeneous boundary values on the solution field |
| Steady-state field prediction | Predict equilibrium physical fields determined jointly by source terms and boundary conditions |
| Numerical solver acceleration | Replace or augment conventional FEM, FDM, and FVM workflows to improve inference efficiency |
Usage
1. OneCode
Use the online OneCode environment for an intelligent, one-click AI for Science (AI4S) programming experience:
Launch OneCode for one-click AI4S programming
2. Manual Setup
Hardware Requirements
- A GPU or DCU is recommended.
- A CPU can be used for import checks and small-scale pipeline validation, but full training and inference will be slow.
- DCU users must install DTK in advance. DTK 25.04.2 or later, or the OneScience-recommended version for the target cluster, is recommended.
Download the Model Package
modelscope download --model OneScience/BENO --local_dir ./BENO
cd BENO
Set Up the Runtime Environment
DCU Environment
# Activate DTK and Conda first
conda create -n onescience311 python=3.11 -y
conda activate onescience311
# Installation with uv is also supported
pip install onescience[cfd-dcu] -i http://mirrors.onescience.ai:3141/pypi/simple/ --trusted-host mirrors.onescience.ai
GPU Environment
# Activate Conda first
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
# Installation with uv is also supported
pip install onescience[cfd-gpu] -i http://mirrors.onescience.ai:3141/pypi/simple/ --trusted-host mirrors.onescience.ai
Training Data
The OneScience community provides the beno dataset for training. Download it with the command below and verify that the data path in config/config.yaml is configured correctly:
modelscope download --dataset OneScience/beno --local_dir ./data
The complete dataset is also available from the official download link.
Training
Single GPU:
python scripts/train.py
Multiple GPUs:
torchrun --standalone --nnodes=<num_nodes> --nproc_per_node=<num_GPUs> scripts/train.py
Model Weights
This repository will provide weights trained on the BENO dataset in the weights/ directory. The weights will be uploaded soon.
Inference
python scripts/inference.py
Evaluation and Visualization
python scripts/result.py
Official OneScience Resources
| Platform | OneScience Repository | Skills 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 |
Citations and License
- Original BENO paper: BENO: Boundary-embedded Neural Operators for Elliptic PDEs
- This repository retains source attribution and has been adapted for automated execution through OneScience and ModelScope. Before public redistribution, verify the applicable licensing requirements of the upstream project.