Improved Training of Physics-Informed Neural Networks Using Energy-Based Priors: a Study on Electrical Impedance Tomography
Akarsh Pokkunuru, Pedram Rooshenas, Thilo Strauss, Anuj Abhishek, Taufiquar Khan
Abstract
Physics-informed neural networks (PINNs) are attracting significant attention for solving partial differential equation (PDE) based inverse problems, including electrical impedance tomography (EIT). EIT is non-linear and especially its inverse problem is highly ill-posed. Therefore, successful training of PINN is extremely sensitive to interplay between different loss terms and hyper-parameters, including the learning rate. In this work, we propose a Bayesian approach through data-driven energy-based model (EBM) as a prior, to improve the overall accuracy and quality of tomographic reconstruction. In particular, the EBM is trained over the possible solutions of the PDEs with different boundary conditions. By imparting such prior onto physics-based training, PINN convergence is expedited by more than ten times faster to the PDE’s solution. Evaluation outcome shows that our proposed method is more robust for solving the EIT problem. Our code is available at: https://rooshenasgroup.github.io/eit_ebprior.
BibTeX
@inproceedings{
pokkunuru2023improved,
title={Improved Training of Physics-Informed Neural Networks Using Energy-Based Priors: a Study on Electrical Impedance Tomography},
author={Akarsh Pokkunuru and Pedram Rooshenas and Thilo Strauss and Anuj Abhishek and Taufiquar Khan},
booktitle={The Eleventh International Conference on Learning Representations },
year={2023},
url={https://openreview.net/forum?id=zqkfJA6R1-r}
}