Upscaling and Automation: Pushing the Boundaries of Multiscale Modeling through Symbolic Computing

Macroscopic differential equations that accurately account for microscopic phenomena can be systematically generated using rigorous upscaling methods. However, such methods are time-consuming, prone to error, and become quickly intractable for complex systems with tens or hundreds of equations. To ease these complications, we propose a method of automatic upscaling through symbolic computation. By streamlining the upscaling procedure and derivation of applicability conditions to just a few minutes, the potential for democratization and broad utilization of upscaling methods in real-world applications emerges. We demonstrate the ability of our software prototype, Symbolica, by reproducing homogenized advective–diffusive–reactive (ADR) systems from earlier studies and homogenizing a large ADR system deemed impractical for manual homogenization. Novel upscaling scenarios previously restricted by unnecessarily conservative assumptions are discovered, and numerical validation of the models derived by Symbolica is provided.