Reproduce “Regression Trees on Grassmann Manifold for Adapting Reduced-Order Models” on OpenResearch

About this paper

Xiao Liu, Xinchao Liu

A statistical learning framework from the University of Arkansas employs regression trees on Grassmann manifolds to adapt reduced-order models (ROMs) by learning a mapping from input parameters to optimal Proper Orthogonal Decomposition (POD) bases. The method often achieves lower prediction errors than global POD or interpolation, with its effectiveness tied to the correlation between parameter variations and corresponding subspace changes.

Key insights

• Regression trees offer an interpretable statistical method to optimally partition the parameter space, enabling adaptive selection of appropriate POD bases for varying system conditions.
• The effectiveness of learning-based ROM adaptation methods is highly dependent on the underlying correlation between Euclidean distances in the parameter space and Riemannian distances in the subspace.
• A 'locally-global' POD basis derived from a partitioned parameter space can often provide better accuracy than a single global POD basis spanning the entire parameter range.

Summary by alphaXiv.