Data Generation

This repository contains PyTorch code for PDE data generation for Poisson, Helmholtz, Reaction-Diffusion, and Navier-Stokes equationis. The data generation code is adopted respectively from

• NavierStokes: PINO,
• PoissonHelmholtz: neuraloperators-TL-scaling,
• ReactionDiffusion: PDEBench.

Environment

For the necessary packages for generating data for each equation, please follow the environment setup for each paper's repository.

Navier-Stokes

The following example generates data with Reynolds number (re) = 300 and random seed (seed) = 0. In our paper, we utilize re = {100, 300, 500, 800, 1000} for pretraining, re = 300 for training and finetuning, and re = 10000 for out-of-distribution (OOD) testing.

cd NavierStokes
python generate_data.py --seed 0 --re 300 

Poisson and Helmholtz

The following example generates data with diffusion eigenvalue (e1, e2) = [5, 15] for Poisson and wave number (o1, o2) = [5, 15] for Helmholtz.

• Poisson In our paper, we utilize diffusion eigenvalue range (e1, e2) = [1, 20] for pretraining, (e1, e2) = [5, 15] for training and finetuning, and (e1, e2) = [15, 50] for out-of-distribution (OOD) testing.

cd Poisson_Helmholtz
python utils/gen_data_poisson.py --ntrain=2000 --nval=1000 --ntest=1000 \
                    --ng=0 --sparse --n 128 --datapath /datapath --e1 5 --e2 15

• Helmholtz In our paper, we utilize wave number range (o1, o2) = [1, 20] for pretraining, (o1, o2) = [5, 15] for training and finetuning, and (o1, o2) = [15, 20] for out-of-distribution (OOD) testing.

cd Poisson_Helmholtz
python utils/gen_data_helmholtz.py --ntrain=2000 --nval=1000 --ntest=1000 \
                    --ng=0 --sparse --n 128 --datapath /datapath --o1 5 --o2 $15

Reaction-Diffusion

The following example generates data with diffusion coefficients Du = 1e-3, Dv = 5e-3. The coefficients can be altered in the yaml file:

sim:
  Du: 1E-3
  Dv: 5E-3

Then, run the following code to generate data.

cd ReactionDiffusion
python gen_diff_react.py

For the other PDEBench data used in the paper, we download from their DaRUS data repository.