This is implementation of physics-informed VAE of the paper: PI-VAE: Physics-Informed Variational Auto-Encoder for stochastic differential equations( https://arxiv.org/abs/2203.11363 )

1. SDE training data construction

1.2 low dimension

cd lib
python training_data.py --case='ODE' --kl=1.0 --fl=0.2 --mesh_size=400

1.2 high dimension imbalance

cd lib
python training_data.py --case='ODE_khigh' --kl=0.02 --fl=1.0 --mesh_size=400 --data_size=5000 
python training_data.py --case='ODE_fhigh' --kl=1.0 --fl=0.02 --mesh_size=400 --data_size=5000

2. Numerical Experiments

2.1 ODE problem

cd examples 
python SDE.py --case='ODE' --u_sensor=2 --k_sensor=17 --f_sensor=21 --mesh_size=400 --epoch=2000 
python SDE.py --case='ODE' --u_sensor=6 --k_sensor=6 --f_sensor=21 --mesh_size=400 --epoch=2000 
python SDE.py --case='ODE' --u_sensor=11 --k_sensor=1 --f_sensor=21 --mesh_size=400 --epoch=2000

2.2 high dimension problem

cd examples 
python SDE.py --case='ODE_khigh' --u_sensor=2 --k_sensor=51 --f_sensor=21 --mesh_size=400 --epoch=2000 --data_size=5000
python SDE.py --case='ODE_fhigh' --u_sensor=2 --k_sensor=17 --f_sensor=51 --mesh_size=400 --epoch=2000 --data_size=5000

If you make advantage of the PI-VAE in your research, please consider citing our paper in your manuscript:

@article{ZHONG2023115664,
title = {PI-VAE: Physics-Informed Variational Auto-Encoder for stochastic differential equations},
journal = {Computer Methods in Applied Mechanics and Engineering},
volume = {403},
pages = {115664},
year = {2023},
issn = {0045-7825},
doi = {https://doi.org/10.1016/j.cma.2022.115664},
url = {https://www.sciencedirect.com/science/article/pii/S0045782522006193},
author = {Weiheng Zhong and Hadi Meidani},
}