# Physics-informed-vibe-coding1
**Repository Path**: hbwei/physics-informed-vibe-coding1
## Basic Information
- **Project Name**: Physics-informed-vibe-coding1
- **Description**: No description available
- **Primary Language**: Unknown
- **License**: Not specified
- **Default Branch**: main
- **Homepage**: None
- **GVP Project**: No
## Statistics
- **Stars**: 0
- **Forks**: 0
- **Created**: 2026-06-24
- **Last Updated**: 2026-06-24
## Categories & Tags
**Categories**: Uncategorized
**Tags**: None
## README
# Physics-Informed Vibe Coding
**首个采用 Vibe Coding 理念进行科学机器学习（PINNs · PIELM · 随机特征方法 · 神经算子）研究的开源仓库**
The first open-source repository for Scientific Machine Learning research — PINNs, PIELM, Random Feature Methods, Neural Operators, and beyond — via the Vibe Coding paradigm
[](https://github.com/xgxgnpu/Physics-informed-vibe-coding)
[](LICENSE)
[](https://github.com/google/jax)
[](https://www.python.org/)
[](https://developer.nvidia.com/cuda-toolkit)
**Xiong Xiong (熊雄)** · Northwestern Polytechnical University (NWPU)
AI4PDE · Physics-Informed Deep Learning · Data-Driven Discovery
[Google Scholar](https://scholar.google.com.hk/citations?user=j1M9tkwAAAAJ) · [ResearchGate](https://www.researchgate.net/profile/Xiong-Xiong-19) · [Email](mailto:xiongxiongnwpu@mail.nwpu.edu.cn)
---
## Philosophy
> **Vibe Coding & Vibe Researching** — Humans discover and formulate the important scientific problems; AI agents write code, execute experiments, and automatically optimize the computation pipeline; humans verify, validate, and accept the final results. Not a single line of code is written by hand.
We believe the future of computational research lies in a clear division of labor between human intellect and AI capability. **Humans** bring domain expertise to identify meaningful problems, design solution strategies, and make critical judgments on result quality. **AI agents** handle the entire implementation cycle — from writing code and running experiments to tuning hyperparameters and generating visualizations. This closed-loop workflow enables researchers to focus on scientific insight rather than engineering overhead. Every algorithm in this repository is implemented in **JAX** with GPU acceleration, and each case is fully reproducible with saved data, figures, and model checkpoints.
> **Vibe Coding & Vibe Researching** — 人类负责发现并提出重要科学问题，AI 智能体负责编程、执行实验与自动优化计算过程，最终由人类核对、验证并验收结果。全程不手写一行代码，（尝试）完成完整的复杂科研项目。
本项目提供一系列**完整、自包含的 JAX-GPU 实现**，覆盖科学机器学习（Scientific Machine Learning）领域的前沿算法，包括 PINNs、物理信息极限学习机（PIELM）、随机特征方法、神经算子等，并配套详细的中文学术教程。**人类**凭借领域知识发现有价值的科学问题、设计求解策略、把控结果质量；**AI 智能体**承担从代码编写、实验运行到超参调优、可视化生成的全链路工作。这一闭环协作模式使研究者得以专注于科学洞察，而非工程细节。
## Contents
| # | Algorithm | Directory | Tutorial | Status |
|---|-----------|-----------|----------|--------|
| 1 | **NTK-PINN** — Neural Tangent Kernel adaptive weighting | [`NTK-PINN-jax/`](NTK-PINN-jax/) | [NTK-PINN 教程](tutorials/NTK-PINN-tutorial.md) | Done |
| 2 | **MultiScale-PINN** — Multi-scale Fourier feature networks for PDEs | [`MultiScalePINN_jax/`](MultiScalePINN_jax/) | 待发布 | Done |
| 3 | **VS-PINN** — Variable-Scaling PINN for Navier-Stokes | [`VSPINN_jax/`](VSPINN_jax/) | [VS-PINN 教程](tutorials/VSPINN/VSPINN-tutorial.md) | Done |
| 4 | **GW-PINN** — Gradient-Weighted adaptive loss balancing | [`GradientWeighted_PINN_jax/`](GradientWeighted_PINN_jax/) | [GW-PINN 教程](tutorials/GradientWeighted-PINN/GradientWeighted-PINN-tutorial.md) | Done |
| 5 | **Scale-PINN** — Evolutionary regularization for high-Re flows | [`ScalePINN-jax/`](ScalePINN-jax/) | 待发布 | Done |
| 6 | **Maxwell-PINN (No BO)** — Pure PINN for 2D EM scattering (Helmholtz + ABC) | `MaxwellPINN_jax/` | 待发布 | Done |
| 7 | **TINN** — Time-Induced Neural Networks with Levenberg-Marquardt for 1D Burgers | `TINN_jax/` | 待发布 | Done |
| 8 | **RFM** — Random Feature Method for PDEs (non-iterative least-squares solver) | [`RFM_jax/`](RFM_jax/) | 待发布 | Done |
## Dependencies
`jax`, `jaxlib` (CUDA), `optax`, `matplotlib`, `numpy`, `scipy`
## How to Run
Each case directory contains a single self-contained `.py` file:
```bash
cd NTK-PINN-jax/case2_wave1d/
python wave1d_ntk_pinn.py
```
```bash
cd MultiScalePINN_jax/case1_heat1d/
python heat1d_multiscale_pinn.py
```
```bash
cd VSPINN_jax/case1_ns2d/
python ns2d_vspinn_pinn.py
```
```bash
cd GradientWeighted_PINN_jax/case2_klein_gordon/
python klein_gordon_gw_pinn.py
```
```bash
cd ScalePINN-jax/case1_ldc_re7500/
python ldc_re7500_scalepinn.py
```
```bash
cd RFM_jax/case1_stokes_2d/
python stokes_2d_rfm.py
```
All results (data `.txt`, figures `.png`, checkpoints `.pkl`) are saved automatically.
## License
MIT
## Citation
If you find this repository useful, please consider citing it:
```bibtex
@software{xiong2026vibecoding,
author = {Xiong, Xiong},
title = {Physics-Informed Vibe Coding: Scientific Machine Learning in JAX via Human-AI Collaboration},
year = {2026},
publisher = {GitHub},
url = {https://github.com/xgxgnpu/Physics-informed-vibe-coding},
note = {PINNs, PIELM, Random Feature Methods, Neural Operators, and beyond}
}
```
You may also cite the following related works:
```bibtex
@article{WANG2022110768,
title={When and why PINNs fail to train: A neural tangent kernel perspective},
author={Wang, Sifan and Yu, Xinling and Perdikaris, Paris},
journal={Journal of Computational Physics},
volume={449},
pages={110768},
year={2022},
doi={https://doi.org/10.1016/j.jcp.2021.110768},
publisher={Elsevier}
}
@article{WANG2021113938,
title={On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networks},
author={Wang, Sifan and Wang, Hanwen and Perdikaris, Paris},
journal={Computer Methods in Applied Mechanics and Engineering},
volume={384},
pages={113938},
year={2021},
doi={https://doi.org/10.1016/j.cma.2021.113938},
publisher={Elsevier}
}
@article{xiong2025high,
title={High-frequency flow field super-resolution via physics-informed hierarchical adaptive Fourier feature networks},
author={Xiong, Xiong and Lu, Kang and Zhang, Zhuo and Zeng, Zheng and Zhou, Sheng and Hu, Rongchun and Deng, Zichen},
journal={Physics of Fluids},
volume={37},
number={9},
year={2025},
publisher={AIP Publishing}
}
@article{xiong2025j,
title={J-PIKAN: A physics-informed KAN network based on Jacobi orthogonal polynomials for solving fluid dynamics},
author={Xiong, Xiong and Lu, Kang and Zhang, Zhuo and Zeng, Zheng and Zhou, Sheng and Deng, Zichen and Hu, Rongchun},
journal={Communications in Nonlinear Science and Numerical Simulation},
pages={109414},
year={2025},
publisher={Elsevier}
}
@article{xiong2025separated,
title={Separated-variable spectral neural networks: a physics-informed learning approach for high-frequency pdes},
author={Xiong, Xiong and Zhang, Zhuo and Hu, Rongchun and Gao, Chen and Deng, Zichen},
journal={arXiv preprint arXiv:2508.00628},
year={2025}
}
@article{chen2022rfm,
title={Bridging Traditional and Machine Learning-based Algorithms for Solving PDEs: The Random Feature Method},
author={Chen, Jingrun and Chi, Xurong and E, Weinan and Yang, Zhouwang},
journal={Journal of Machine Learning},
volume={1},
number={3},
pages={268--298},
year={2022},
doi={10.4208/jml.220726}
}
@article{dwivedi2020pielm,
title={Physics Informed Extreme Learning Machine (PIELM)--A rapid method for the numerical solution of partial differential equations},
author={Dwivedi, Vikas and Srinivasan, Balaji},
journal={Neurocomputing},
volume={391},
pages={96--118},
year={2020},
doi={10.1016/j.neucom.2019.12.099}
}
@article{zhang2025legend,
title={Legend-KINN: A Legendre Polynomial-Based Kolmogorov-Arnold-Informed Neural Network for Efficient PDE Solving},
author={Zhang, Zhuo and Xiong, Xiong and Zhang, Sen and Wang, Wei and Zhong, Yanxu and Yang, Canqun and Yang, Xi},
journal={Expert Systems with Applications},
pages={129839},
year={2025},
publisher={Elsevier}
}
```