shuaidyip / ro-norm

A general reduced-order neural operator for spatio-temporal predictive learning on complex spatial domains

This repository contains code accompanying our paper ["A general reduced-order neural operator for spatio-temporal predictive learning on complex spatial domains"]. For questions, feel free to contact us ([email protected]).

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-Case6 can be found in here.

Case1-Burgers.mat
├── Input: U_initial  4000*415*100
└── Output: U_field   4000*415
---------------------------------------------
Case2-Wave.mat
├── Input: U_field   2000*100*506
└── Output: U_source  2000*100
---------------------------------------------
Case3-Layout.mat
├── Input: layout  1200*1168
└── Output: T_field 1200*1168*151
---------------------------------------------
Case4-Qianyuan.mat
├── Input: Tair_time   600*151*6
└── Output: T_field       600*151*2743
---------------------------------------------
Case5-Qianyuan.mat
├── Input: T_field       600*151*2743
└── Output: D_field   600*2743
---------------------------------------------
Case6-BloodFlow.mat
├── Input: `BC_time`(500*121*6)
└── Output: `velocity_x`(500*1656*121),`velocity_y`,`velocity_z`

Usage

Here we present the code for case1, and the code for other cases is similar. you can run the codes by executing Parallel_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 Parallel_main.py 

Results

Case1

Case2

Case3

Case4

Case5

Case6