A Topology-Preserving Coreset for Kernel Regression in Scientific Visualization

Modern simulations and observations generate vast amounts of data, fueling a growing interest in replacing discrete data with continuous surrogate models, such as functional models and implicit neural networks, to enhance data storage, transfer, analysis, and visualization. To that end, kernel regression is a well-known class of non-parametric techniques useful for surrogate modeling. In this paper, we propose a new framework to use coresets for kernel regression-a small dataset that is used as a proxy for the original data-in scientific visualization. Using kernel regression as a surrogate for scientific data, we construct an optimized coreset that is both compact and highly accurate, reducing errors from randomly-sampled and grid-based coresets by orders of magnitude. We evaluate our framework on large spatial datasets and demonstrate that it incurs negligible error while preserving the underlying topological features.