Reduced order modeling for flow and transport problems with Barlow Twins self-supervised learning
This work addresses the challenge of flexible and accurate reduced order modeling for computational fluid dynamics, particularly in porous media, though it appears incremental by building on existing autoencoder and self-supervised learning methods.
The authors tackled the performance gap between linear and nonlinear reduced order modeling for flow and transport problems by proposing a unified framework using Barlow Twins self-supervised learning with autoencoders, achieving comparable results to POD-based approaches for linear subspaces and outperforming previous deep learning ROMs for nonlinear manifolds.
We propose a unified data-driven reduced order model (ROM) that bridges the performance gap between linear and nonlinear manifold approaches. Deep learning ROM (DL-ROM) using deep-convolutional autoencoders (DC-AE) has been shown to capture nonlinear solution manifolds but fails to perform adequately when linear subspace approaches such as proper orthogonal decomposition (POD) would be optimal. Besides, most DL-ROM models rely on convolutional layers, which might limit its application to only a structured mesh. The proposed framework in this study relies on the combination of an autoencoder (AE) and Barlow Twins (BT) self-supervised learning, where BT maximizes the information content of the embedding with the latent space through a joint embedding architecture. Through a series of benchmark problems of natural convection in porous media, BT-AE performs better than the previous DL-ROM framework by providing comparable results to POD-based approaches for problems where the solution lies within a linear subspace as well as DL-ROM autoencoder-based techniques where the solution lies on a nonlinear manifold; consequently, bridges the gap between linear and nonlinear reduced manifolds. Furthermore, this BT-AE framework can operate on unstructured meshes, which provides flexibility in its application to standard numerical solvers, on-site measurements, experimental data, or a combination of these sources.