Autoencoder-based Dimensionality Reduction for Accelerating the Solution of Nonlinear Time-Dependent PDEs: Transport in Porous Media with Reactions

TL;DR

This paper presents a convolutional autoencoder approach to reduce dimensionality and accelerate the simulation of nonlinear transport in porous media, addressing computational challenges in high-fidelity PDE models.

Contribution

It introduces a nonlinear compression technique using a convolutional autoencoder specifically for transport in porous media, improving simulation efficiency.

Findings

Achieved low MSE (~1e-3) on validation data.

Model performs well for larger time steps on unseen parameters.

Lower accuracy observed at earlier times, indicating room for architecture improvements.

Abstract

Physics-based models often involve large systems of parametrized partial differential equations, where design parameters control various properties. However, high-fidelity simulations of such systems on large domains or with high grid resolution can be computationally expensive for the accurate evaluation of a large number of parameters. Reduced-order modeling has emerged as a solution to reduce the dimensionality of such problems. This work focuses on a nonlinear compression technique using a convolutional autoencoder for accelerating the solution of transport in porous media problems. The model demonstrates successful training, achieving a mean square error (MSE) on the order of \num{1e-3} for the validation data. For an unseen parameter set, the model exhibits mixed performance; it achieves acceptable accuracy for larger time steps but shows lower performance for earlier times. This issue could potentially be resolved by fine-tuning the network architecture.