Projection-based Model Reduction: Formulations for Physics-based Machine Learning
This talk describes approaches at the intersection of projection-based model reduction and machine learning. Our data-driven formulation learns a low-dimensional model directly from data, but through the lens of projection-based model reduction. The state-space for learning is derived using physics-based variable transformations that expose problem structure. Case studies demonstrate the importance of embedding physical constraints within learned models, especially in engineering settings where the amount of training data may be limited.