Peridynamics for Data Estimation, Image Compression/Recovery, and Model Reduction

The existing interpolation and regression methods are highly data-specific, challenge-specific, or approach-specific. Peridynamic approach provides a single mathematical framework for diverse data-sets and multi-dimensional data manipulation and model order reduction. The mathematical framework based on the Peridynamic Differential Operator (PDDO) provides a unified approach to transfer information within a set of discrete data, and among data sets in multi-dimensional space. The robustness and capability of this approach have been demonstrated by considering various real or fabricated data concerning two- or three-dimensional applications. The numerical results concern interpolation of real data in two and three dimensions, interpolation to approximate a three-dimensional function, adaptive data recovery in three-dimensional space, recovery of missing pixels in an image, adaptive image compression and recovery, and free energy evaluation through model reduction.