# Robust Reference Frame Extraction from Unsteady 2D Vector Fields with Convolutional Neural Networks

## TL;DR

This paper introduces a neural network approach for extracting stable reference frames from unsteady 2D vector fields, improving robustness over traditional methods and providing a new benchmark dataset for the community.

## Contribution

It presents an end-to-end CNN method for feature extraction in unsteady vector fields and creates a synthetic benchmark dataset for deep learning in this domain.

## Key findings

- Neural network outperforms optimization-based methods in stability.
- Synthetic dataset enables large-scale training and evaluation.
- Method successfully applied to unseen fluid flow data.

## Abstract

Robust feature extraction is an integral part of scientific visualization. In unsteady vector field analysis, researchers recently directed their attention towards the computation of near-steady reference frames for vortex extraction, which is a numerically challenging endeavor. In this paper, we utilize a convolutional neural network to combine two steps of the visualization pipeline in an end-to-end manner: the filtering and the feature extraction. We use neural networks for the extraction of a steady reference frame for a given unsteady 2D vector field. By conditioning the neural network to noisy inputs and resampling artifacts, we obtain numerically stabler results than existing optimization-based approaches. Supervised deep learning typically requires a large amount of training data. Thus, our second contribution is the creation of a vector field benchmark data set, which is generally useful for any local deep learning-based feature extraction. Based on Vatistas velocity profile, we formulate a parametric vector field mixture model that we parameterize based on numerically-computed example vector fields in near-steady reference frames. Given the parametric model, we can efficiently synthesize thousands of vector fields that serve as input to our deep learning architecture. The proposed network is evaluated on an unseen numerical fluid flow simulation.