• Corpus ID: 247614679

Reduced order modeling for flow and transport problems with Barlow Twins self-supervised learning

@inproceedings{Kadeethum2022ReducedOM,
  title={Reduced order modeling for flow and transport problems with Barlow Twins self-supervised learning},
  author={Teeratorn Kadeethum and Francesco Ballarin and Daniel O'Malley and Youngsoo Choi and Nikolaos Bouklas and Hongkyu Yoon},
  year={2022}
}

• T. Kadeethum, F. Ballarin, +3 authors H. Yoon
• Published 11 February 2022
• Computer Science

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. We illustrate that a proficient construction of the latent space is key to achieving these results, enabling us to map these latent spaces using regression models. The proposed framework achieves a relative error of 2% on average and 12% in the worst-case scenario (i.e., the training data is small, but the parameter space is large.). We also show that our framework provides a speed-up of 7× 106 times, in the best case, and 7× 103 times on average compared to a finite element solver. 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.