Code for PCSM

We provide the experimental code for Darcy Flow, Navier-Stokes, Airfoil, and Plasticity. Additional code will be provided in the next version.

Environment Installation

Create and activate an Anaconda Environment:

conda create -n PCSM python=3.8
conda activate PCSM

Install required packages with the following commands:

pip install -r requirement.txt

Data Preparation

Download the dataset from the following links, and then unzip them in a specific directory.

• Darcy Flow: Google Driver
• Navier-Stokes: Google Driver
• Airfoil: Google Driver
• Plasticity: Google Driver

Experiment Running

Run the experiments with the following scripts.

• Darcy Flow:

bash ./exp_scripts/darcy.sh [The Directory of Downloaded Data] 
# The Provided Directory should be like: XXX/Darcy

• Navier-Stokes:

bash ./exp_scripts/darcy.sh [The Directory of Downloaded Data]
# The Provided Directory should be like: XXX/Navier-Stokes

• Airfoil:

bash ./exp_scripts/ns.sh [The Directory of Downloaded Data]
# The Provided Directory should be like: XXX/naca

• Plasticity:

bash ./exp_scripts/plasticity.sh [The Directory of Downloaded Data]
# The Provided Directory should be like: XXX/plasticity

Acknowledge

We thank the following open-sourced projects, which provide the basis of this work.

• https://github.com/neuraloperator/neuraloperator
• https://github.com/gengxiangc/NORM
• https://github.com/thuml/Transolver
• https://github.com/nmwsharp/nonmanifold-laplacian