Hypernetwork-based Meta-Learning for Low-Rank Physics-Informed Neural Networks (NeurIPS 2023)

Introduction

This repository contains pytorch implementation for our NeurIPS 2023 (spotlight) paper:

Hypernetwork-based Meta-Learning for Low-Rank Physics-Informed Neural Networks

Experimental environment settings.

Run the following code before starting the experiment.

conda env create -f env.yaml
conda activate meta

Data generation

You can generate dataset for train / validation / test. Run code in the folder "data_gen".

     [ Code ]                   [ Description of code ]

python gen_conv.py : Code for generating convection equation data
python gen_diff.py : Code for generating diffusion equation data
python gen_reac.py : Code for generating reaction equatinon data
python gen_cd.py   : Code for generating Convection-Diffusion equation data
python gen_rd.py   : Code for generating Reaction-Diffusion equation data
python gen_cdr.py  : Code for generating Convection-Diffusion-Reaction data

Set the initial condition using "u0_str" parser. (you can select following option : sin_1, gauss, gauss_pi_2, etc...)

[ u0_str ]

sin_1       : 1+sin(x)
gauss       : Gaussian distribution with STD=pi/4.
gauss_pi_2  : Gaussian distribution with STD=pi/2.

Train

Run the following code for Hyper-LR-PINN training / testing.

     [ Code ]              [ Description of code ]

python train_meta.py    : Code for Hyper-LR-PINN training [phase1]
python train_full.py    : Code for Hyper-LR-PINN (Full rank) training [phase2]
python train_adap.py    : Code for Hyper-LR-PINN (Adaptive rank) training [phase2]

Detailed settings can be changed in config.py

For example, if you run the following code,

python train_meta.py --epoch 20000 --pde_type convection --init_cond sin_1 --start_coeff_1 1 --end_coeff_1 20
python train_adap.py --epoch 10000 --pde_type convection --init_cond sin_1 --start_coeff_1 1 --end_coeff_1 20 --target_coeff_1 10
python train_full.py --epoch 10000 --pde_type convection --init_cond sin_1 --start_coeff_1 1 --end_coeff_1 20 --target_coeff_1 10

You can train/test the Hyper-LR-PINNs in the setting below.

[ Experimental setting ]

phase1 : 20000 epoch
phase2 : 10000 epoch
pde type : convection equation,
initial condition : 1+sin(x),
target equation : beta=10 (convection equation),
meta-learning range : beta $\in$ [1, 20]

Test

In additaon, we attach checkpoint of Hyper-LR-PINN (.pt file) If you want to check it quickly, run the following code below.

     [ Code ]                   [ Description of code ]

python test.py  : Code for testing Hyper-LR-PINN (Adaptive) (30~40 range, convection equation)

For example, if you run the following code,

python test.py --pde_type convection --init_cond sin_1 --start_coeff_1 30 --end_coeff_1 40 --target_coeff_1 40

You can test the Hyper-LR-PINN (Adaptive rank) quickly. (beta=40)

Other code

Brief description of the other code files.

    [ Code ]        [ Description of code ]
    
    model.py   :  Hyper-LR-PINN model. (phase1, phase2)
    utils.py   :  PDE residual loss