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.

Scalar field comparison is a fundamental task in scientific visualization. In topological data analysis, we compare topological descriptors of scalar fields-such as persistence diagrams and merge trees-because they provide succinct and robust abstract representations. Several similarity measures for topological descriptors seem to be both asymptotically and practically efficient with polynomial time algorithms, but they do not scale well when handling large-scale, time-varying scientific data and ensembles. In this paper, we propose a new framework to facilitate the comparative analysis of merge trees, inspired by tools from locality sensitive hashing (LSH). LSH hashes similar objects into the same hash buckets with high probability. We propose two new similarity measures for merge trees that can be computed via LSH, using new extensions to Recursive MinHash and subpath signature, respectively. Our similarity measures are extremely efficient to compute and closely resemble the results of existing measures such as merge tree edit distance or geometric interleaving distance. Our experiments demonstrate the utility of our LSH framework in applications such as shape matching, clustering, key event detection, and ensemble summarization.