Inverse Physics-Informed Neural Networks for transport models in porous materials

TL;DR

This paper introduces an adaptive inverse PINN approach for transport models in porous materials, effectively estimating parameters in diffusion and advection-diffusion-reaction problems with improved convergence.

Contribution

It proposes an adaptive weighting scheme for loss components in inverse PINNs, enhancing convergence and robustness in transport parameter estimation.

Findings

Adaptive loss weighting improves convergence in inverse PINNs.

The method is scalable to different transport models.

Robustness is demonstrated across various test cases.

Abstract

Physics-Informed Neural Networks (PINN) are a machine learning tool that can be used to solve direct and inverse problems related to models described by Partial Differential Equations. This paper proposes an adaptive inverse PINN applied to different transport models, from diffusion to advection-diffusion-reaction problems. Once a suitable PINN is established to solve the forward problem, the transport parameters are added as trainable parameters. We find that, for the inverse problem to converge to the correct solution, the different components of the loss function (data misfit, initial conditions, boundary conditions and residual of the transport equation) need to be weighted adaptively as a function of the training iteration (epoch). Similarly, gradients of trainable parameters are scaled at each epoch accordingly. Several examples are presented for different test cases to support our PINN architecture and its scalability and robustness.