AutoKE

The PyTorch Source code for An automatic knowledge embedding framework for scientific machine learning.

Instructions

To run the code for conducting the experiments in the paper, follow the script and optional parameters below:

python main.py [--system] [--seed] [--N_f] [--optimizer_name] [--lr] [--xgrid] [--nt] [--u0_str] [--layers] [--epoch-adam] [--activation][--visualize] [--save_model] [--data-path] [--name] [--mode] [--auto] [--pretrain-model-path]

Possible arguments:
--system              system of study (default:rd; also support kdv equation, viscous gravity current(vgc), and new system defined by yourself)
--seed                used to reproduce the results (default: 0)
--N_f                 number of points to sample from the interior domain (default: 1000)
--optimizer_name      optimizer to use, currently supports L-BFGS
--lr                  learning rate (default: 1.0)
--xgrid               size of the xgrid (default: 256)
--nt                  Number of points in the tgrid (default 100)
--u0_str              initial condition (default: 'sin(x)'; also supports 'gauss' for reaction/reaction-diffusion)
--layers              number of layers in the network (default: '50,50,50,50,1')
--epoch-adam          epoch numbers for adam optimizer (default:10000)
--activation          activation for the network (default: 'tanh')
--visualize           option to visualize the solution (default: False)
--save_model          option to save the model (default: False)
--data-path           path of data
--name                job name 
--mode                mode of the NN (default: traing; also support "test"  and "pretrain")
--auto                option to implement physical constraints automatically (default: False)
--pretrain-model-path checkpoint path for pretraining

Example

For solving the KdV equation, you need to write a JSON format configuration file in accordance with the prescribed format. See kdv.json in folder config/. It contains the system name, ASCII representation of the equaiton, and some subcomponents for the equation.

Training scripts:

python main.py --system kdv --layers 2,128,128,128,128,128,128,1 --mode train --name kdv --epoch-adam 20000 --auto  

To be updated:

New features and cases

Reference resources

https://github.com/tensordiffeq/TensorDiffEq
https://github.com/a1k12/characterizing-pinns-failure-modes