Dimensionality Reduction and Reduced Order Modeling for Traveling Wave Physics.

We develop an unsupervised machine learning algorithm for the automated discovery and identification of traveling waves in spatio-temporal systems governed by partial differential equations (PDEs). Our method uses sparse regression and subspace clustering to robustly identify translational invariances that can be leveraged to build improved reduced order models (ROMs). Invariances, whether translational or rotational, are well known to...