Scaling laws and competitiveness of purely data-driven PMMs

Characterize the scaling laws of purely data-driven parametric matrix models and determine whether they are competitive with modern artificial neural-network methods.

Background

Purely data-driven PMMs extend the PMM framework beyond settings in which the governing equations are known. The thesis reports promising performance but does not establish their comparative behavior across model size, dataset size, input dimension, or computational budget.

Resolving their scaling behavior and comparative competitiveness is also relevant to partially data-driven PMMs, which combine learned components with known physical structure.