BPINNs
Model Overview
BPINNs (Bayesian Physics-Informed Neural Networks) incorporate physical-equation constraints into Bayesian neural networks to jointly estimate equation solutions and predictive uncertainty from noisy data. This model package provides an example for solving a one-dimensional Laplace equation:
u_xx + pi^2 sin(pi x) = 0, x in [0, 1]
u(x) = sin(pi x)
Paper: B-PINNs: Bayesian physics-informed neural networks for forward and inverse PDE problems with noisy data
https://doi.org/10.1016/j.jcp.2020.109913
Model Description
BPINNs are trained jointly on observational data, boundary conditions, and PDE residuals. By default, the model is optimized with Adam and then refined with L-BFGS. During inference, predictive means and standard deviations can be computed from multiple parameter states stored in a checkpoint. The default training workflow produces only one optimized state; full Bayesian uncertainty quantification requires posterior parameter states obtained through Hamiltonian Monte Carlo (HMC), variational inference, or ensemble sampling.
Use Cases
| Use Case | Description |
|---|---|
| One-dimensional Laplace equation | Train the solution jointly from observation points, boundary points, and collocation points |
| PDE modeling with noisy data | Fit noisy observations subject to physical constraints |
| Optimizer comparison | Compare the effects of Adam and L-BFGS on PINN convergence |
| Posterior prediction | Compute predictive means and standard deviations from multiple parameter states |
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 can accelerate full training; a CPU is sufficient for pipeline validation.
- DCU users must install DTK and a PyTorch environment compatible with the target cluster.
Download the Model Package
modelscope download --model OneScience/BPINNs --local_dir ./BPINNs
cd BPINNs
Set Up the Runtime Environment
DCU Environment
# Activate DTK and Conda 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
# 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
pip install onescience[cfd-gpu] -i http://mirrors.onescience.ai:3141/pypi/simple/ --trusted-host mirrors.onescience.ai
Training Data
This example automatically generates interior observation points, boundary points, PDE collocation points, and a test grid from the analytical solution; no external data files are required. The number of observation and collocation points, noise level, and computational domain can be configured in conf/config.yaml.
Training
python scripts/train.py
By default, training produces the base weights at weight/bpinn_laplace1d.pt and saves the training history to result/training_history.npz.
Model Weights
This repository provides weights trained on the one-dimensional Laplace equation in the weight/ directory.
L-BFGS Refinement
python scripts/refine.py
By default, refinement produces weight/bpinn_laplace1d_refined.pt.
Inference, Evaluation, and Visualization
python scripts/inference.py
Inference loads the refined weights when available and otherwise falls back to the base weights. Predictions and visualizations are saved to result/. Model, training, loss, and inference parameters can all be modified in conf/config.yaml.
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
- Yang, L., Meng, X., and Karniadakis, G. E. B-PINNs: Bayesian physics-informed neural networks for forward and inverse PDE problems with noisy data. Journal of Computational Physics, 425, 109913, 2021.
- This model package is released under the Apache-2.0 license and retains attribution to the original paper.