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

Area of Science:

• Computational Fluid Dynamics
• Machine Learning
• Scientific Computing

Background:

• Reduced Order Models (ROMs) are crucial for accelerating complex simulations.
• Existing Deep Learning ROM (DL-ROM) methods excel at nonlinear manifolds but struggle with linear ones.
• Convolutional layers in DL-ROM limit applicability to structured meshes.

Purpose of the Study:

• To develop a unified data-driven ROM that bridges the performance gap between linear and nonlinear manifold approaches.
• To enhance DL-ROM by incorporating Barlow Twins (BT) self-supervised learning for improved latent space representation.
• To enable DL-ROM application on unstructured meshes for broader usability.

Main Methods:

• A novel framework combining autoencoders (AE) with Barlow Twins (BT) self-supervised learning.
• Utilizing a joint embedding architecture to maximize information content in the latent space.
• Benchmarking against Proper Orthogonal Decomposition (POD) and existing DL-ROM on natural convection in porous media problems.

Main Results:

• The proposed BT-AE framework achieves performance comparable to POD for linear subspaces and DL-ROM for nonlinear manifolds.
• Demonstrated significant improvement in latent space construction for accurate regression mapping.
• Achieved an average relative error of 2% and a worst-case of 12%.
• Reported speed-ups of up to [Formula: see text] times compared to finite element solvers.
• Successfully operated on unstructured meshes, enhancing flexibility.

Conclusions:

• The BT-AE framework effectively bridges the gap between linear and nonlinear ROMs.
• Proficient latent space construction is key for accurate predictions and mapping.
• The method offers computational efficiency and flexibility for diverse data sources and mesh types.