Advantages of Weak-Form Equation Learning in Reduced-Order Models for Parametric PDEs
Presenter
January 6, 2025
Abstract
"Recent advancements in data-driven modeling highlight that adopting a weak formulation of model equations significantly improves noise robustness across various computational methods. This presentation explores how the weak form enhances the LaSDI (Latent Space Dynamics
Identification) algorithm, a recently developed data-driven
reduced order modeling technique. We introduce a weak form-based extension of LaSDI, WLaSDI - Weak-form Latent Space
Dynamics Identification. WLaSDI first compresses data,
then projects onto the test functions and learns the local
latent space models. Notably, WLaSDI demonstrates significantly enhanced robustness to noise. WLaSDI obtains
the local latent space using weak-form equation learning.
Compared to the standard SINDy used in LaSDI, the variance reduction of the weak form guarantees a robust and precise latent space recovery, hence allowing for a fast, robust, and
accurate simulation."