Introduction

This project provides codes for paper Solving multiscale steady radiative transfer equation using neural networks with uniform stability. The main difficulty comes from the significantly varying magnitude of the Knusen number. To overcome the multiscale issue, we propsed an novel PINN loss based on the micro macro decomposition for the steady state of radiative transfer equation(RTE).

Usage of code

The following codes require some input parameters. The epsi is the Knudsen number, bc_loss_weight is the weight of boundary loss function, Nx is number of grid points on x direction, nl is number of hidden layers, nr is number of neurons in each hidden layer.

1D isotropic case with constant inflow B.C.

python rte_rg.py epsi bc_loss_weight Nx nl nr

1D isotropic case with boundary layer.

Firstly, compute the boundary layer corrector

python hsp_rb_msi.py

Then

python rte_rg_hsp.py epsi bc_loss_weight Nx nl nr

1D anisotropic case with constant boundary

python rte_rg_aniso.py epsi bc_loss_weight Nx nl nr

1D anisotropic case with boundary layer

Firstly, compute the boundary layer corrector

python hsp_rb_at_msi.py

Then

python rte_rg_hsp_aniso.py epsi bc_loss_weight Nx nl nr

1D two materials.

python rte_rg_sigma.py epsi bc_loss_weight Nx nl nr

1D scattering function

python rte_rg_epsix.py

1D Nonlinear RTE with constant boundary

python rte_rg_nonl.py epsi bc_loss_weight Nx nl nr

1D Nonlinear RTE with boundary layer

First, compute boundary layer corrector

python hsp_nonl_msi.py

Then

python rte_rg_nonl_hsp.py epsi bc_loss_weight Nx nl nr

2D RTE with constant boundary

python rte_2D.py epsi bc_loss_weight Nx nl nr

2D RTE with square boundary involved boundary layer

Compute auxiliary hsp for each grid points on boundary parallelly

python hsp_rb_aux_para.py

Train 2D boundary layer corrector

python hsp_2d_aux_limit.py

Then

python rte_2d_hsp.py epsi bc_loss_weight Nx nl nr

Figures in paper

hsp_1d

python hsp_rb_load.py

hsp_2d_H and hsp_2d_reflec

python load_Gamma_aux.py

rg_1d_epsi1, rg_1d_epsizpzz1 and hsp_1d_bl_epsi1

python load_rte.py

hsp_1d_bl_epsizppz1

python load_rte_nonuni,py

hsp_1d_two_materials

python load rte_sigma.py

hsp_1d_ani_eps_1_g5, hsp_1d_ani_eps_zpzz1_g5_bl and hsp_1d_ani_eps_1_g5_bl

python load_rte_aniso.py

hsp_1d_ani_eps_zpzz1_g5_bl

python load_rte_aniso_nonuni.py

hsp_1d_nonl__eps_1_bl and hsp_1d_nonl_eps_1

python load_rte_nonl.py

hsp_1d_nonl_eps_zpzz1 and hsp_1d_nonl_eps_zpzz1_bl

python load_rte_nonl_epsi.py

hsp_2d_bl_eps1, hsp_2d_analytic

python load_rte_2D.py

hsp_2d_bl

python rg_2D_hsp_load.py