A Topology-Preserving Coreset for Kernel Regression in Scientific Visualization.

Area of Science:

• Data Science
• Scientific Visualization
• Machine Learning

Background:

• Modern scientific simulations produce large datasets, necessitating efficient data handling.
• Surrogate models, like functional models and implicit neural networks, are increasingly used for data compression and analysis.
• Kernel regression is a powerful non-parametric method for building surrogate models.

Purpose of the Study:

• To develop a new framework for utilizing coresets in kernel regression for scientific visualization.
• To create a compact and accurate coreset for representing large scientific datasets.
• To reduce the error associated with surrogate modeling in scientific data.

Main Methods:

• Proposed a novel framework integrating coresets with kernel regression.
• Developed an optimized coreset construction method for scientific data.
• Evaluated the framework on large-scale spatial datasets.

Main Results:

• The proposed coreset framework significantly reduces approximation errors compared to random sampling and grid-based methods.
• The optimized coresets are compact yet highly accurate representations of the original data.
• Negligible error was observed in the evaluation, preserving essential topological features.

Conclusions:

• The coreset-based kernel regression framework offers a highly accurate and efficient solution for scientific data surrogate modeling.
• This approach enhances data storage, transfer, analysis, and visualization capabilities.
• The method shows promise for handling the increasing volume of data from scientific simulations and observations.