# Scientific Data Interpolation with Low Dimensional Manifold Model

## TL;DR

This paper introduces a low dimensional manifold model for scientific data interpolation, effectively handling missing data from regular and irregular samplings, and demonstrating its utility across various scientific fields.

## Contribution

It presents a novel variational approach leveraging low dimensionality of data patches, solved via alternating minimization and graph Laplacian discretization.

## Key findings

- Effective data interpolation from irregular samplings
- Improved data compression capabilities
- Versatile application across scientific disciplines

## Abstract

We propose to apply a low dimensional manifold model to scientific data interpolation from regular and irregular samplings with a significant amount of missing information. The low dimensionality of the patch manifold for general scientific data sets has been used as a regularizer in a variational formulation. The problem is solved via alternating minimization with respect to the manifold and the data set, and the Laplace-Beltrami operator in the Euler-Lagrange equation is discretized using the weighted graph Laplacian. Various scientific data sets from different fields of study are used to illustrate the performance of the proposed algorithm on data compression and interpolation from both regular and irregular samplings.