Publications

Greedy fiedler spectral partitioning for data-driven discrete exterior calculus

Huang, Andy H.; Trask, Nathaniel A.; Brissette, Christopher; Hu, Xiaozhe

The data-driven discrete exterior calculus (DDEC) structure provides a novel machine learning architecture for discovering structure-preserving models which govern data, allowing for example machine learning of reduced order models for complex continuum scale physical systems. In this work, we present a Greedy Fiedler Spectral (GFS) partitioning method to obtain a chain complex structure to support DDEC models, incorporating synthetic data obtained from high-fidelity solutions to partial differential equations. We provide justification for the effectiveness of the resulting chain complex and demonstrate its DDEC model trained for Darcy flow on a heterogeneous domain.