# Advanced reduced-order models for moisture diffusion in porous media

## TL;DR

This paper compares two model reduction techniques, Spectral-ROM and PGD, demonstrating their effectiveness in accurately and efficiently modeling moisture diffusion in porous media with significantly reduced computational cost.

## Contribution

The article provides a detailed methodology for applying Spectral-ROM and PGD to moisture diffusion problems, serving as a numerical benchmark for future reduced-order modeling in porous materials.

## Key findings

- Both methods achieve around tenfold reduction in model order.
- The approaches provide solutions with less than 1% error compared to reference models.
- They effectively handle linear, non-linear, and parametric moisture diffusion problems.

## Abstract

It is of great concern to produce numerically efficient methods for moisture diffusion through porous media, capable of accurately calculate moisture distribution with a reduced computational effort. In this way, model reduction methods are promising approaches to bring a solution to this issue since they do not degrade the physical model and provide a significant reduction of computational cost. Therefore, this article explores in details the capabilities of two model-reduction techniques - the Spectral Reduced-Order Model (Spectral-ROM) and the Proper Generalised Decomposition (PGD) - to numerically solve moisture diffusive transfer through porous materials. Both approaches are applied to three different problems to provide clear examples of the construction and use of these reduced-order models. The methodology of both approaches is explained extensively so that the article can be used as a numerical benchmark by anyone interested in building a reduced-order model for diffusion problems in porous materials. Linear and non-linear unsteady behaviors of unidimensional moisture diffusion are investigated. The last case focuses on solving a parametric problem in which the solution depends on space, time and the diffusivity properties. Results have highlighted that both methods provide accurate solutions and enable to reduce significantly the order of the model around ten times lower than the large original model. It also allows an efficient computation of the physical phenomena with an error lower than 10^{-2} when compared to a reference solution.