pinn-implementation

Requirements

• uv

Usage

# for burgers' equation
cd ./burgers_continuous_forward
uv run train.py # start training

# for pitzDaily
cd ./pitzDaily/
cp -r /your/path/to/VTK ./ # copy the VTK folder generate by OpenFOAM
uv run VTKtoNumpy.py # transform VTK data into numpy format 
uv run train.py

Config

pitzDaily

• n_epochs(int): The maximum epochs when training
• early_stop(int): If loss not decrease for <early_stop> epochs, the training will enter the second phase of training or stop training(if the training have been in second phase)
• save_path(str): Where you save the model parameters
• system:
  • viscosity(float): The physics system's viscosity
• pde_param:
  • continuity_param(int): The weight of continuity equation loss in total PDE loss
  • ns_param(int): The weight of Navier-stokes equation loss in total PDE loss.
• loss_param:
  • pde_loss_param(int): The weight of PDE loss in total physics loss
  • ic_loss_param(int): The weight of IC loss in total physics loss
  • bc_loss_param(int): The weight of BC loss in total physics loss
• fourier_param:
  • mapping_dim(int): The feature length after Fourier embedding.
  • sigma(float): Still need research

Result

Burgers' equation