Uncertainty-Aware Deep Neural Representations for Visual Analysis of Vector Field Data

TL;DR

This work addresses the challenge of quantifying and communicating prediction uncertainty in deep learning–driven vector-field visualization. It proposes uncertainty-aware implicit neural representations (INRs) built on a SIREN-based architecture and evaluates two uncertainty estimation strategies: Deep Ensemble and Monte Carlo Dropout. Through 2D and 3D flow datasets, the approach demonstrates informative reconstructions, uncertainty maps, and uncertainty-aware visualizations of streamlines and critical points, enhancing robustness and interpretability. The study highlights trade-offs: Ensemble yields higher reconstruction fidelity at the cost of longer training time, while MCDropout provides a faster, single-model alternative with comparable uncertainty patterns. Overall, the work delivers practical uncertainty-aware visualization techniques for complex flow analyses and offers guidance for choosing between uncertainty estimators in scientific visualization settings.

Abstract

The widespread use of Deep Neural Networks (DNNs) has recently resulted in their application to challenging scientific visualization tasks. While advanced DNNs demonstrate impressive generalization abilities, understanding factors like prediction quality, confidence, robustness, and uncertainty is crucial. These insights aid application scientists in making informed decisions. However, DNNs lack inherent mechanisms to measure prediction uncertainty, prompting the creation of distinct frameworks for constructing robust uncertainty-aware models tailored to various visualization tasks. In this work, we develop uncertainty-aware implicit neural representations to model steady-state vector fields effectively. We comprehensively evaluate the efficacy of two principled deep uncertainty estimation techniques: (1) Deep Ensemble and (2) Monte Carlo Dropout, aimed at enabling uncertainty-informed visual analysis of features within steady vector field data. Our detailed exploration using several vector data sets indicate that uncertainty-aware models generate informative visualization results of vector field features. Furthermore, incorporating prediction uncertainty improves the resilience and interpretability of our DNN model, rendering it applicable for the analysis of non-trivial vector field data sets.

Figures (16)

• Figure 1: The schematic of the MCDropout-enabled INR model which uses a residual block-based MLP architecture. A dropout layer is added at the last residual block to generate uncertainty estimates during inference time. The INR architecture for the Ensemble method is identical to this, except there is no dropout layer.
• Figure 2: Volume visualization of the magnitude of reconstructed vector fields using MCDropout and Ensemble methods for Hurricane Isabel data set. The ground truth is shown in Fig. \ref{['isabel_GT']}. We observe that both methods produce visually comparable results.
• Figure 3: Volume visualization of the magnitude of reconstructed vector fields using MCDropout and Ensemble methods for Tangaroa data set. The ground truth is shown in Fig. \ref{['tangaroa_GT']}. We observe that both methods produce visually comparable results.
• Figure 4: Visualization of uncertainty and error fields for Hurricane Isabel data set. The MSE and prediction uncertainty is estimated at each grid point between the predicted and ground truth vectors for MCDropout and Ensemble methods. Fig. \ref{['isabel_MSE_MCD']} and Fig. \ref{['isabel_MSE_ENS']} show the rendering of MSE fields, and Fig. \ref{['isabel_Uncrt_MCD']} and Fig. \ref{['isabel_Uncrt_ENS']} present the rendering of uncertainty fields. We observe that the locations with higher MSE correspond to similar spatial regions for both methods. In contrast, the vortex region is detected as a region with higher prediction uncertainty for both methods.
• Figure 5: Visualization of uncertainty and error fields for Tangaroa data set. The MSE and prediction uncertainty are estimated at each grid point between the predicted and ground truth vectors for MCDropout and Ensemble methods. Fig. \ref{['tangaroa_MSE_MCD']} and Fig. \ref{['tangaroa_MSE_ENS']} show the rendering of MSE fields, and Fig. \ref{['tangaroa_Uncert_MCD']} and Fig. \ref{['tangaroa_Uncert_ENS']} present the rendering of uncertainty fields. Results indicate that regions with higher MSE align spatially for both methods, while areas with higher prediction uncertainty are more widespread for MCDropout compared to the Ensemble method.