Uncertainty-Informed Volume Visualization using Implicit Neural Representation

TL;DR

Uncertainty poses a challenge for DNN-based volume visualization of scalar fields. The authors propose uncertainty-aware implicit neural representations built on SIREN, and evaluate two deep uncertainty estimation techniques, Deep Ensemble and Monte Carlo Dropout, to produce pixel-wise uncertainty maps during volume rendering. Across Teardrop, Isabel, and Combustion datasets, they show that uncertainty-informed INR reconstructions achieve high PSNR and robust RMSE, with Ensemble providing strongest accuracy at the cost of training time, while MCDropout offers a lighter alternative. The work enables trust-aware visualization of real-world volumetric data and suggests directions for extending to time-varying and multivariate data.

Abstract

The increasing adoption of Deep Neural Networks (DNNs) has led to their application in many challenging scientific visualization tasks. While advanced DNNs offer impressive generalization capabilities, understanding factors such as model prediction quality, robustness, and uncertainty is crucial. These insights can enable domain scientists to make informed decisions about their data. However, DNNs inherently lack ability to estimate prediction uncertainty, necessitating new research to construct robust uncertainty-aware visualization techniques tailored for various visualization tasks. In this work, we propose uncertainty-aware implicit neural representations to model scalar field data sets effectively and comprehensively study the efficacy and benefits of estimated uncertainty information for volume visualization tasks. We evaluate the effectiveness of two principled deep uncertainty estimation techniques: (1) Deep Ensemble and (2) Monte Carlo Dropout (MCDropout). These techniques enable uncertainty-informed volume visualization in scalar field data sets. Our extensive exploration across multiple data sets demonstrates that uncertainty-aware models produce informative volume visualization results. Moreover, integrating prediction uncertainty enhances the trustworthiness of our DNN model, making it suitable for robustly analyzing and visualizing real-world scientific volumetric data sets.

Figures (9)

• Figure 1: The schematic of the MCDropout-enabled INR model which uses a residual block-based MLP architecture. Dropout layer is added at the last two residual blocks to generate uncertainty estimates during inference time. The INR architecture for the Ensemble method is identical to this, except there are no dropout layers.
• Figure 2: Volume visualization of Teardrop data set for three representative MC-sampled fields from the MCDropout method (top row) and three representative fields generated from three ensemble members (bottom row) for the Ensemble method. The ground truth is shown in Fig. \ref{['teardrop_final']}. It is observed that individual MC sampled fields produce inaccurate visualization at the thin central segment of the Teardrop data, highlighted by red dotted circles for the MCDropout method. In contrast, the visualization produced by individual ensemble members are more accurate.
• Figure 3: Visualization of ground truth, expected (averaged) volume visualization by the MCDropout method, and expected (averaged) volume visualization by the Ensemble method of Teardrop data set. We observe that both MCDropout and Ensemble methods produce comparable and high-quality rendering results.
• Figure 4: Prediction uncertainty and error maps of Teardrop data. Both methods produce high uncertainty and error at the thin central segment (highlighted by red dotted circles). Such uncertainty information can readily help the users to identify regions where the model is under-confident. We further observe that the teardrop's boundary also shows higher uncertainty and error, indicating that both methods are also unable to confidently predict the sharp boundary regions.
• Figure 5: Prediction uncertainty visualization of Teardrop data set for individual RGB color channels. We observe that the prediction uncertainty patterns are comparable across all three color channels for the MCDropout and Ensemble methods.