gengxiangc/norm

Learning Neural Operators on Riemannian Manifolds

This repository contains code accompanying our paper "Learning Neural Operators on Riemannian Manifolds".

Dependencies & packages

Dependencies:

• Python (tested on 3.8.11)
• PyTorch (tested on 1.8.0)

Additionally, we need an open-source Python package Lapy (https://github.com/Deep-MI/LaPy/tree/main) for differential geometry on triangle and tetrahedra meshes, which is used to calculate LBO basis. If you fail to install it, try to add the lapy folder included in our source code into your path.

Data

The datasets of Case1-Case3 can be found in datasets folder. You can download the dataset(s) of Case4 and Case5 from here.

Case1-DarcyFlow.mat
├── Input: `c_field`(1200*2290)
└── Output: `u_field`(1200*2290)
---------------------------------------------
Case2-Turbulence.mat
├── Input: `Input`(400*2673)
└── Output: `Output`(400*2673)
---------------------------------------------
Case3-HeatTransfer.mat
├── Input: `input`(300*186)
└── Output: `output`(300*7199)
---------------------------------------------
Case4-Composites.mat
├── Input: `T_field`(1200*8232)
└── Output: `D_field`(1200*8232)
---------------------------------------------
Case5-BloodFlow.mat
├── Input: `BC_time`(500*121*6)
└── Output: `velocity_x`(500*1656*121),`velocity_y`,`velocity_z`

Usage

For all cases, you can directly run the codes by executing main.py to quickly obtain the results. Note that each experiment is repeated five times, the same setup as in our paper. Each case also retains the setting of hyperparameters in the paper.

python main.py 

Additionally, we provide the Calculate_LBO_basis.py in datasets folder to calculate the LBO basis for Case3, Case4 and Case5. The calculation of Case1 and Case2 are embedded in the corresponding main.py.

Results

Case1, Case2 and Case3

---

Video for Case5

Blood_flow_NORM.mp4

Publication

If you found this repository useful, please consider citing our paper:

@misc{chen2023learning,
      title={Learning Neural Operators on Riemannian Manifolds}, 
      author={Gengxiang Chen and Xu Liu and Qinglu Meng and Lu Chen and Changqing Liu and Yingguang Li},
      year={2023},
      eprint={2302.08166},
      archivePrefix={arXiv},
}