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](https://openreview.net/forum?id=ZZTkLDRmkg) # 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](https://web-2069360198568017922-iaaj.ksai.scnet.cn:58043/home) ## 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 ```bash modelscope download --model OneScience/BENO --local_dir ./BENO cd BENO ``` ### Set Up the Runtime Environment **DCU Environment** ```bash # 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** ```bash # 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: ```bash modelscope download --dataset OneScience/beno --local_dir ./data ``` The complete dataset is also available from the [official download link](https://drive.google.com/file/d/11PbUrzJ-b18VhFGY_uICSciCkeGrsaTZ/view). ### Training Single GPU: ```bash python scripts/train.py ``` Multiple GPUs: ``` torchrun --standalone --nnodes=