Learning Similarity Metrics for Volumetric Simulations with Multiscale CNNs

TL;DR

This paper introduces VolSiM, a multiscale CNN-based similarity metric for 3D simulation data, addressing high-dimensional data challenges with invariance and robustness evaluations.

Contribution

It presents the first learning-based volumetric similarity metric designed specifically for high-dimensional simulation data, incorporating entropy-based ground truth and multiscale CNN architecture.

Findings

VolSiM effectively measures similarity across diverse simulation data.

The method demonstrates invariance to rotation and scale transformations.

Robustness is confirmed through tests on turbulence and real-world data.

Abstract

Simulations that produce three-dimensional data are ubiquitous in science, ranging from fluid flows to plasma physics. We propose a similarity model based on entropy, which allows for the creation of physically meaningful ground truth distances for the similarity assessment of scalar and vectorial data, produced from transport and motion-based simulations. Utilizing two data acquisition methods derived from this model, we create collections of fields from numerical PDE solvers and existing simulation data repositories. Furthermore, a multiscale CNN architecture that computes a volumetric similarity metric (VolSiM) is proposed. To the best of our knowledge this is the first learning method inherently designed to address the challenges arising for the similarity assessment of high-dimensional simulation data. Additionally, the tradeoff between a large batch size and an accurate correlation computation for correlation-based loss functions is investigated, and the metric's invariance with respect to rotation and scale operations is analyzed. Finally, the robustness and generalization of VolSiM is evaluated on a large range of test data, as well as a particularly challenging turbulence case study, that is close to potential real-world applications.